Given that US military is larger than the next 6 largest armies combined, is this to prepare for the possibility of nations with the next 6 largest armies jointly declaring war on US?
What are some non-political (i.e. practical) reasons that justify enlarging the US army?
The typical answers for military spending are all exactly what you didn't ask for. I'll recap them briefly just for background:
One common explanation is that military spending is good for the economy. Intuitively, this seems reasonable. However, recent studies using more sophisticated econometric models have shown the relationship is statistically insignificant.
A second explanation is public safety. The programmatic outcome of defense spending is protection from other military threats. A time series study of military spending in developing nations concluded that both external and civil wars do result in an increase in military spending (Dunne and Perlo-Freeman, 2003)
Finally, veterans benefits constitute a large portion (though no where near the majority) of defense spending. According to the Congressional Budget Office, this spending is increasing because the number of veteran's has quickly increased since 2000. Additionally, the proportion of veteran's receiving disability and other benefits has sharply increased.
Given that US military is larger than the next 6 largest armies combined
This is not true. The United States military is more expensive than the next six most expensive militaries. The US army is not even the largest, much less bigger than the six largest not counting the US.
According to World Atlas, the US has the second largest military in the world. It's well behind China and a bit ahead of India and North Korea. A bit more research suggests that this is active military personnel.
According to Wikipedia, which bases its numbers on The Military Balance from the International Institute for Strategic Studies, the US has the seventh largest total military, including active, reserve, and paramilitary personnel.
The United States spends more per soldier. Some of this is better gear, but some of it is simple costs. The United States has a comparatively high cost of living when set against countries with larger populations. In particular, India is less than a third the cost of living as the United States. And China is a bit over half.
The US is twentieth (according to the World Bank) in percentage of GDP spent on the military. This is behind, for example, Russia.
Twice during the twentieth century, Germany was one of the main belligerents in a World War. After the second one, the allies, including the United States, banded together to keep it from forming a new army. To this day, the US has military bases in Germany.
For similar reasons, the US has maintained a military presence in Japan, which continues to this day.
The US participated in a civil war in Korea and maintains a military presence in South Korea to this day.
The US, which has one of the two largest Jewish populations of any country, gives military aid to Israel (the other top two country). This also may explain some of its participation in other conflicts in the Middle East.
The US was at war for the entire Obama presidency. This was the first time that a president served a full two terms while at war.
The US has the third largest population of any country, and the highest cost of living of the nine largest population countries.
It's also worth noting that war is expensive. The US has not fought a large scale war against a comparable opponent since the Cold War. In an actual war with another country, the US military budget would likely increase. Defense spending in World War II passed 40% of GDP, more than ten times what the US spends now.
Some of the comments suggest that I'm arguing that the US is not the most powerful military in the world. I'm not. What I'm pointing out is that the US is not more powerful militarily than the next six most powerful militaries. In particular, the Chinese and Russian militaries are, combined, probably more powerful than the US military. And certainly if you mixed in three of the NATO countries besides the US, those five countries would be more powerful militarily than the US.
The correct statistic by which the US beats the next six countries combined is expense. The United States has the most expensive military in the world by a large margin. Just a few years ago, it was actually more expensive than all the rest of the world's militaries. However, as I noted, this does not actually mean that it is six times more powerful any more than North Korea's size means that it is twice as powerful. Neither size nor expense are good proxies for military power.
I've ignored that you used the word "army" rather than military, even though that makes this worse. Most of the expense of the US military is in things like the Air Force and Navy rather than the Army per se. I've been assuming that you meant military.
Both the US and Russia have sufficient nuclear weapons to end civilization as we know it. Other countries may as well. So put aside any significant use of nuclear weapons, as a country that makes major use of nuclear weapons will lose any conflict (along with every other country).
Quality does not always beat quantity. Take the US Civil War for an example. The South had the higher quality army. Most of the officers were from the South. They pretty consistently took fewer casualties than the North did. Yet the North won in the end.
This isn't to say that North Korea would be able to outlast the US in a war. The US has more capacity to increase its army than North Korea does. But it might mean that China could outlast the US. Or maybe not.
In actual, non-nuclear war two militaries that are evenly matched make for the worst war. Because both sides are close to parity, neither will win quickly. The longer a war lasts, the more damage it does to both sides. So militaries would prefer to engage when clearly more powerful than their opponents. Often more resources will reduce the long term cost of the conflict.
What could the US buy with a higher defense budget than it has now?
This may be the question that people find interesting. I didn't really get into this in my original answer, as it seems obvious once one realizes that the US is not that far ahead of other countries. But if you want some specific examples of things that are not include in the current US budget, consider
Updated nuclear missiles. The US has been decreasing the size of its nuclear arsenal since the 1980s. Some believe that the current arsenal might be getting to the point where it will start failing. They want to replace missiles that are forty or more years old with newer, more reliable missiles.
More updated planes. Many of the US planes were bought decades ago. During the last election, pictures were posted of planes with no engines, etc. It's not clear that this isn't purely business as usual (once planes are no longer built, it makes sense to dismantle some to fix others), but some have called for an increase in new planes that don't have to be repaired immediately.
Two front war. In 2008, the US was participating in wars in both Afghanistan and Iraq. In 2016, the US could not have actively done so. It would have had to choose between the two countries. The provisional plans called for fighting a holding action in one theater while actively trying to win in the other.
This may not seem that important, but it matches actual experience. It is relatively common for the US to be involved in two fronts. Not just the recent Afghanistan/Iraq example, but World War II's Pacific and Atlantic theaters. Or the Civil War, where there was a Mississippi theater and a Virginia theater. And of course the risk that a country might be more willing to act if the US was already at war, knowing the US couldn't fight another war at the same time.
More volunteers. The US could pay more on recruiting and wages. During the Iraq war, the US called up not just the Reserves but the National Guard. Swapping out more people who don't want to be active military with people who do would improve morale.
Increasing the number of reservists would also help. They provide a trained base if ever the draft were reinstituted to fight a large scale conflict.
More tanks. Russia and China have more tanks than the US (source). Of course, tanks have not been that useful in recent conflicts. Most vehicles are used to move infantry rather than to fight themselves. But this is an area where the US actually lags.
Better logistics. I've spoken with veterans who had trouble getting supplied with food while in Iraq. I doubt this was widespread, but it was a problem. More money spent on supplies and getting supplies to where they are needed could be helpful in future conflicts.
Better armor. Many military vehicles capable of operating in Afghanistan (rough, mountainous terrain) weren't armored, leaving them vulnerable to improvised explosive devices (IEDs). This lead to the Donald Rumsfeld quote: "As you know, you go to war with the army you have, not the army you might want or wish to have at a later time." Some would prefer to equip the army with what they wish it would have.
What are some non-political (i.e. practical) reasons that justify enlarging the US army?
The U.S. has a clearly best in the world Air Force (especially in air superiority and long range bombing and long range operations with air tankers) and Navy (especially projecting force with Air Craft Carriers and cruise missile launching ships), but merely a par for the course Army in terms of combat superiority vis-a-vis other militaries. The U.S. is strong in blue sea naval combat ship to ship, but weak in its capacity to handle asymmetric naval warfare in a cost efficient manner (e.g. it uses $1 billion warships to deal with pirates in $100,000 speedboats), it is weak in anti-mine warfare, its surface combatants are somewhat vulnerable to modern submarines, and both the Air Force and the Navy have underinvested in fire support and logistics support for ground troops. The U.S. Army is also much better at some tasks (forward observer, signals intelligence, eye in the sky recon, artillery, medical care for troops injured in battle, long distance marksmanship) by international standards than others (patrolling to suppress an insurgency in a culturally different place, foreign language resources, logistics, building community support for their side), relative to their near peers. The technology of the U.S. land based nuclear missile force is profoundly outdated (it runs computers that use 8" floppy disks with 1970s class computers), and the discipline of the forces operating those missiles has been disgraceful in recent times producing multiple scandals, so there is a need for improvement in technology and training in this area, but the raw number of powerful nuclear weapons in the arsenal is far in excess of any reasonable military necessity for their use, suggesting cuts, and it isn't obvious that all three legs of the nuclear triad are really necessary (i.e. long range bombers, submarine based ballistic missiles and land based ballistic missiles).
The U.S. Army is not particularly large given historical precedents or its peer countries or size as a nation and has a pretty low tooth to tail ratio. The U.S. Army can field only about 100,000 ground troops in a foreign war without calling up reserve/national guard forces to the limit if it isn't fighting somewhere that it already has a large foreign military base (e.g. Japan, Korea, Germany). Foreign basing commitments and a large proportion of support specialties and the need for troop rotation limit how many troops it can deploy at once. One can legitimately imagine conflicts in which more than 100,000 ground troops might need to be deployed in foreign wars at once. The U.S. military has about 25%-30% fewer active duty personnel than it did during the Cold War. Only about a third of the combatants in the Navy can be deployed at any given time at sea and it takes months to move a ship from one theater of combat to another. The Air Force has planes that provide far more capabilities than it was designed for because the number of kills per sortie has dramatically increased with smart bombs, and the Air Force has secured air superiority in every recent conflict in a fairly short time period after which the need for combat aircraft falls dramatically, and it can very rapidly move planes from theater to theater so unless to completely different foreign wars are at the several week long air to air combat air superiority phase at exactly the same time, redundancy isn't important.
The Air Force and Navy can defeat enemies, but not hold territory or take control of territory on land. It takes ground troops to do that and the U.S. Army can provide ground troops.
It is almost certainly the case that the relative investments in different subparts of the U.S. military is not optimal. The relative investments in U.S. force structure are remarkably similar to those at the beginning of the Reagan Administration (probably the most notable exceptions are increased investments in drones and reduced investments in Army units that deploy in tanks that have been replaced with less heavily armored ground troop units), despite major technological changes that have changed the military effectiveness of different kinds of units relative to each other (e.g. far more accurate and automated artillery and bombing and missile technologies, and far more automated new ships). Even if the total force size and budget remained the same, there are good practical reasons for reducing the investment in some kinds of forces while increasing the investment in other kinds of forces. For example, transport plane and refueling tankers are used very intensely by the Air Force while long range bombers get very light use. We invest a lot in amphibious assault training and equipment but no one in the world has used that approach in a militarily important way since the Korean War. There are more efficient ways to destroy enemy surface combatants than with $1 billion destroyers that go 20 mph at cruise speed and have all accommodations for a large crew for many months on board at all times and there has been extremely little ship to ship combat between major surface combatants for decades despite the fact that we invest a lot of money in this mission.
Enlarging the U.S. Army creates lots of good jobs with benefits for working to middle-middle class men, especially in Red States, who no college degrees but are willing to work hard to make a living and who feel patriotic (i.e. Trump voters whom even Democrats admit are facing hard economic times in the current economy). It is also an important mechanism for social class mobility (see, e.g. "The Hillbilly Elegy") not just because of skill and education training but due to character building and allowing less mature HS students to mature enough to be reading for higher education or committing to a skilled trade after getting out. The military is the only job in the economy that pays you more if you have a larger family in a basically socialist economic arrangement.
Military procurement and military bases provide an economic boost to communities that have defense contractors and bases respectively.
In this answer I have deliberately refrained from considering relative investments in the Marines v. the U.S. Army which is a close thing and technical and doesn't have a clear answer. Some arguments applicable to the Army also apply to the Marines (who are also ground troops), while others do not, and many of our peers have no real equivalent to the Marines. The U.S. Army was cut more deeply after the Cold War than the Marines, and historically the Marines have grown less rapidly in wartime than the U.S. Army. There are also good practical reasons not to enlarge the U.S. Army (or the U.S. military or parts of it) as well, but those are beyond the scope of the question.
