In the 1920s, why did the United States decide to prohibit alcohol instead of some other substance? There were many other substances available, presumably any of them could have been banned. Why was alcohol the one chosen?
Prohibition did not come about because people were seeking to ban anything and decided to select alcohol. Rather, prohibition was the culmination of a temperance movement that had developed in the US for decades.
People had been seeking to ban alcohol for well over a century because its use was widespread and so were its effects. No other substance came close to alcohol in this regard.
Alcohol was banned by Congress through Amendment 18 in 1917 because of Protestant protest groups and grassroot campaigns from several Woman's Rights Movement organizations. The Wikipedia article sums everything up fairly well.
LSD was discovered by a man named Albert Hofmann in 1938, so it came afterwards.
Extasy was invented in 1914 in Germany, so America had no clue it existed.
During Prohibition, substances such as heroin and cocaine, as well as plants such as Cannabis, were either completely legal, or at least regulated. The Harrison Narcotics Tax Act of 1914 had put restrictions on cocaine and heroin. The Wikipedia article for cocaine says:
While this act [Harrison Narcotics] is often seen as the start of prohibition, the act itself was not actually a prohibition on cocaine, but instead set up a regulatory and licensing regime. The Harrison Act did not recognize addiction as a treatable condition and therefore the therapeutic use of cocaine, heroin or morphine to such individuals was outlawed – leading the Journal of American Medicine to remark, "[the addict] is denied the medical care he urgently needs, open, above-board sources from which he formerly obtained his drug supply are closed to him, and he is driven to the underworld where he can get his drug, but of course, surreptitiously and in violation of the law."
After Prohibition began, Congress started to use various "tax-acts" to outlaw substances such as cocaine and heroin. The Jones-Miller Act put very harsh restrictions on opoids and cocaine. Whether these laws were Constitutional was questioned for a while, but by 1924, the U.S. Supreme Court had declared in Whipple v. Martinson that:
There can be no question of the authority of the State in the exercise of its police power to regulate the administration, sale, prescription and use of dangerous and habit-forming drugs, such as are named in the statute. The right to exercise this power is so manifest in the interest of the public health and welfare, that it is unnecessary to enter upon a discussion of it beyond saying that it is too firmly established to be successfully called in question.
In 1933, Congress and several states ratified the Constitution with Amendment 21 to take alcohol out of the hands of gang members and murderers, finally putting an end to the failed Prohibition.
Through the 13 years of Prohibition, Cannabis remained legal in almost every state. Only California (1914) had outlawed Cannabis prior to Prohibition to combat a growing "Mexican problem".
By the 1930's, Cannabis became popular in the black Jazz scene, and Cab Calloway even had a popular song called "Reefer Man"
In 1934, Harry J. Anslinger became the head of the newly founded Federal Bureau of Narcotics. Anslinger, along with William Randolph Hearst, began a smear campaign against Cannabis. It became known in popular media as "the Devil's Weed" and a monstrous drug that sent people on violent rampages. This era is known as "Reefer Madness", which is also the title of a movie produced in 1936. You can find plenty of quotes from Anslinger, but here are a few examples:
"Colored students at the Univ. of Minn. partying with (white) female students, smoking [marijuana] and getting their sympathy with stories of racial persecution. Result: pregnancy."
"Two Negros took a girl fourteen years old and kept her for two days under the influence of hemp. Upon recovery she was found to be suffering from syphilis."
It wasn't until the Marihuana Tax Act of 1937 that Cannabis became completely outlawed in the United States. Hemp was also made illegal, but that's another story...
In 1969, the Marihuana Tax Act was challenged by Timothy Leary in Leary v. United States. Leary claimed that the tax-act required self incrimination, because in order to possess Cannabis, you had to have a stamp; but in order to get a stamp, you must possess illegal Cannabis. Leary won, so a year later Congress enacted the Controlled Substance Act.
Instead of requiring a tax stamp to possess Cannabis and other substances, Congress used the Commerce Clause of the Constitution to claim any drug that is possessed or manufactured could potentially effect the interstate market. Therefore, Congress has effectively taken over intrastate commerce, so that they can ban absolutely anything they want for any reason.
So, alcohol was actually causing a problem, and Congress acted by amending the Constitution. That's what the people wanted and that's what Congress was supposed to do. Then Congress took it upon themselves to ban any other substances they deemed bad. It was unconstitutional, so they just made up a new rule. That's basically why alcohol was prohibited instead of other substances.
Cocaine and heroin became illegal in 1915. LSD and XTC did not exist, at least not as something used recreationally.
The main reason that they chose alcohol over other drugs was how widespread its use was. Virtually everyone knew of at least one drunk. The number of dope fiends was far smaller and after all, those drugs were often already illegal.
Note that Prohibition was not passed by referendum but by legislative action. The federal Congress passed it and sufficient state legislatures ratified it.
To build on a summary in Phoog's answer:
Alcohol was considered the root cause of spousal abuse (the driving reason behing Women's temperance league).
Almost everyone drank alcohol, for historical and hygienic reasons, making impact of alcohol immeasurably higher.
Saloons led to political corruption.
So there are two parts to the answer.
First, why ban anything?
At the time, women were just starting to see the possibilities of voting. At the time men created the laws, they approve them, they enforced them. Women had no part in it except to have to follow those laws. Now women were just starting to "get the vote". This was very important, as it meant that politicians now had to answer for things that originally, were thought well of and now were not. For example, got caught out with a mistress at the local night club. The guys may, at the diner table go "Aww that's too bad", but at the night club, congratulate the senator. Men may have voted for this guy because he had 12 mistresses. Women on the other hand, would not have found this acceptable. Keep in mind that at the time, the U.S. Government's stance on prostitution was limited to quarantining women suspected of having STDs.
So as women started to enter the ranks of voters. Their concerns became more "listened to".
Enter the "Temperance" movement. The general idea being that Americans, needed to sober up, in may ways. Fathers need to spend time at home with children. Families needed to return to churches. Americans in general needed to cut back on the extravagances of the "Progressive" era and really get back to work, etc. etc. The US had a real problem. And the temperance movement was about "Stop whoring, Stop drinking, Get back to work, and Get back to church."
Women, in general, approved and supported, this temperance movement. At a time when women didn't work, and their lives, and the lives of their children, were only as good as their husbands could provide, the temperance movement gave them a way to see that their husbands came home, went to work, and went to church.
You must also understand that women, were largely "uneducated" and "inexperienced" in political matters. While they fought for the right to vote, many had never before actually voted, in any way. Men had all the experienced in this area. With that being said, they also very much knew that once they got the vote, that their voice would count. And many of them focused on educating themselves on making sure their voices counted in the places where it mattered most to them. Home, Family, and morality.
So all of these things come together to form a circumstance where politicians needed to do something to placate the new massive amount of voters. Women, largely didn't care about foreign policy, or tax reform, but if there was a single topic that nearly every women could vote on, it was temperance. So using temperance to please the new or soon to be women voters seemed like a no brainier.
Second Why booze?
On the other side of the gender isle, men too were concerned with the temperance movement. Perhaps they were not as unified or as "active" but it was a very important issue. Businessmen were tired of employees showing up drunk for work, or not at all. Fathers were tired of sons and daughters running off to do the horizontal polka, because of a preceved loss of moral conviction. Men and women didn't really agree on what should be done, but both agreed that something needed to be done.
Thus Everyone starts looking for a culprit. Why is crime up? Why is un-wed pregnancy up? Why are people not showing to work? Why are children left without fathers? Why are people poor? Why are people homeless? Why are all these social problem happening?
And at every turn, no matter where you looked, booze was the bad guy. Bill was drunk when he robbed the store. Jack and Jill were both drunk when they made little Bobbie. Dad wasn't home cause he was out getting drunk. Poor, must have spent all your cash on booze. And so on.
Finally, there was this idea of "noblesse oblige". Simply put, many took it to mean that "I'm better then you so I know whats best for you." (That's not really what it means, but that's how many intreputed it.) I am not a drunk, therefore I know best how to handle the drunks, and it's my responsibility to do so.
The laws of prohibition, were decidedly weak. They were not intended to stop drinking. They were designed to stop irresponsible (low brow) drinking. So men, more accustomed to politics at the time, used prohibition to appease these new/up coming mass of voters, while at the same time address a serious social issue in a way that made the most sense (to them).
Drinking would be reduced, the social issue addressed, and women please (remember this was just about the first time anyone cared about that politically). It was a win all the way around.