According to Fox, President Trump may have ordered troops withdrawn from Syria due to President Erdoğan giving advanced warning of an imminent anti-PKK Turkish invasion. Why would this motivate the US to withdraw, instead of a Turkey-US collaboration? The above source suggests Erdoğan recommended such a withdrawal; why would Turkey seek it?
This is Turkish-US cooperation, as it works out in practice.
Up to now the two countries have been rather at odds over Syria. The US's priorities have been twofold: destroy IS's territorial holdings, and avoid committing US ground forces wherever possible. A side benefit is doing anything to destabilise Syria to prevent Assad from regaining control of the country, since denying Russia and Iran a stable, reliable ally has no downside from the US point of view.
Turkish priorities are somewhat different. Their first priority is preventing the formation of anything resembling a Kurdish state on their border. Anything that weakens Assad is also good since Turkey doesn't really want a stable unfriendly power on their southern border backed by other powerful states, but that's a lower priority.
The US has long wanted Turkey to be more involved in Syria, since they have a competent military that could easily oppose IS and Assad. But Turkey wasn't particularly interested in opposing IS because it doesn't really pose a threat to them. They were happy to keep out of it and let the various factions in the civil war get on with it.
Hence the US had to resort to using the much less capable Kurdish militias and so-called 'moderate opposition' (which was largely a fiction created by wishful thinking or attempts to make things palatable to the US public).
Even last week (around 10th December?) the US announced the construction of new observation posts along the Syrian-Turkish border to help defend their Kurdish allies from Turkish intervene while they dealt with IS, amount with public warnings to Turkey not to take unilateral action against the Kurds.
Two things have changed in the last week. The Syrian Democratic Forces (basically Kurds) announced victory over the last major IS stronghold in northeast Syria. And it became clear that Turkey was going to take unilateral action against the Kurds regardless of what the US wished.
So US policy has pivoted. Now that IS is 'defeated' the Kurds are not needed. If Turkey essentially annexes the Kurdish parts of Syria, they will do a better job of a) securing it against an IS resurgence and b) prevent Assad from regaining control over the whole country. And more importantly, the more of Syria they control, the more leverage they have in the inevitable multi-party negotiations on the future of the country. This serves both the US and Turkeys interests. It isn't so much in the Kurds interests, but apparently they are expendable.
So the US gets of of the way before Turkey comes charging in, and gets to disengage forces entirely from Syria, while still achieving its main objectives. Is just that Turkey becomes its main ally (which was always the preferred plan) rather than the Kurds.
I would argue contra to the accepted answer by @PhillS..
It seems that Turkey has leverage to take advantage of the situation, and seems to have anticipated this type of response from the US government - specifically from Trump.. Not only is Trump clearly deflecting politically, he is in a minority here. The US ground troops are not entrenched, and closing operations can be quick. Trump has repeatedly campaigned and stated his desire to leave Syria. Now with him vulnerable, and with an advantageuos headline with IS beaten, the Turks merely pushed Trump into leaving, and he has used this opportunity to advance his own interests.
The US leaving, I would argue, will not only create a vacuum in northern Syria, but will in deepen cooperation between Turkey and Russia. The Russians now have a strong position to support Turkey, while the US will have no ground presence and no allies within Syria. Russia in fact doesn't need to share power in Syria, it only needs to veneer of influence, and unless Turkey really is willing to deploy massive troops to eradicate the Kurdish claims, which is debatable, both them and the Russians and better off shutting any such possibility by consolidating control of Assad in the area.
At the table, the Russians and Assad can have something significant to offer Turkey - the promise of no Kurdish state in the north. Perhaps this can achieved by Turkish-Russian-Syrian cooperation.
How this situation will play out to the US' advantage is not immediately clear to me at all. The resignation of Mattis seems to confirm that in the eyes of the US Defense Depart. this move weakens the US position.
The US has been supporting Kurdish forces against the organisation that calls itself (in English) "Islamic State of Iraq and the Levant", but is often abbreviated to ISIL, ISIS, or just IS.
The same Kurds that the US has been supporting would be the target of a Turkish intervention. Turkey doesn't like IS, but the Kurdish desire to speak their own language in Turkey is anathema to the Turkish government. The Turkish government has been quite honest about that, saying on January 8 that it will not provide any security guarantees for the Kurds that have been allied with the US against IS and feeling rather insulted by the suggestion that they might.
If the US forces were to turn around and start fighting the Kurds in collaboration with Turkey, they would never again be able to enlist any kind of irregular forces as allies. Even withdrawing will do considerable damage to perceptions of the USA.
I think many actions of Turkey are easier to comprehend if you look at Hitler's actions prior to WW2. Sadly, Erdogan and Hitler have incredibly much in common. If you want to become a dictator, you need an "outgroup". Hitler used the Jews for this; Erdogan takes the Kurds. Erdogan needs to keep this "enemy" in focus to keep himself in power. This "thread" of the Kurds in Syria lets many Turks see in Erdogan a leader and protector. Also, as Phills said in his excellent answer, Erdogan wants his own part of Syria. To close my Hitler-comparison: "Lebensraum im Osten" - Space in the East.
EDIT: As noted, I forgot to mention the role of the US: because of the fact the Erdogan marked the Kurds as the enemy, he really wants to take some aggression towards them. While US-troops support the Kurds, an attack could easily lead to a war with the US. So it's strongly in the interest of Erdogan that the US withdraws their troops, though I wouldn't say that this was the reason for the withdrawal. I don't think that Trump would fear Turkey. But I think it was just an opportune moment to fulfill his promise to get the US troops home.
In Syria, there are three main groups:
- The Syrian government. The United States is not working with them.
- Daesh/Islamic State. The US is actively opposed to them.
- The Kurds. Allies of the US, with US military personnel embedded.
Turkey has a large Kurdish population, particularly in the southeast corner. Turkey claims that Kurdish terrorists are crossing from Syria into Turkey, participating in terrorists acts, and then returning to Syria. So they want to invade and attack the Kurds.
Turkey wants the US to leave, so the Turkish military doesn't accidentally kill US military personnel while attacking the Kurds.
It is not practical for the US and Turkey to work together, as Turkey's target is the very people with whom the US has been working. Both the Kurds and the US have been fighting Daesh. Kurdish terrorism does not threaten the US.
It is unclear what Turkey has offered in exchange for a US withdrawal. Nothing? A commitment to fight Daesh as well as the Kurds? It's also unclear how much the US has been supporting Turkish aims in Syria. Have they been advocating Kurdish extradition of terrorists to Turkey?
Making matters worse, some have asserted that Turkey isn't worried so much about Kurdish terrorism as simply Kurdish separatism. A strong Kurdish group in Syria (and Iraq) makes it easier for Turkish Kurds to assert their independence politically, as they can flee government persecution if necessary.
There have been terrorist actions in Turkey that have been blamed on Kurdish terrorists.
There is probably at least some truth on all sides. Some terrorist actions in Turkey caused by Kurds (possibly acting individually). A lack of support from Syrian Kurds in bringing those to justice. Turkish government attempts to squash political opposition by Turkish Kurds in the name of preventing Kurdish terrorism. These are not mutually exclusive possibilities. They can all be true (to some extent) at the same time. They may not be as true as they are claimed (e.g. the terrorists may not have official support; the Turks may really regard some alleged political enemies as terrorists).
TL;DR: the US and Turkish interests in Syria are opposed. There is no real scope for the two to work together at this time.
What would happen if Turkey decided to push an offensive in Northern Syria.. while US troops were still present? In fact... In all seriousness.. what would happen if US troops were actually and in practice.. forced to actually enter combat with Russia...Iran... Or Turkey.. And those countries responded by not backing down.. but actually using all the force at their disposal?
In short. The US is withdrawing because its presence in Syria is untenable. Turkey's threat to prosecute a war in 'US held territory' regardless of US objection caused the US to evaluate its position in reality.. rather than idealism.
On a level battlefield.. Given time to draw up all forces.. the US would defeat any nation or alliance in conventional warfare. But if open war broke out in Syria.. the us would maybe have 10000 troops on the field in a few days. In that time Russia might have that number of tanks on the field.
And what would happen were the war to escalate to NBC? The US mainland would be at risk.
It was always a mistake to believe that Russia.. Turkey... Iran... Syria or China would back down. Any future war is unwinnable.. and a conventional war in Syria is not something the US could effectively prosecute.
Pulling troops from Syria is simply the right thing to do. It took Turkey's threats to make the sleep walkers in the US military to do the hard sums.. and still there are those who can't wrap their heads around it..
I'm no fan of trump. But he gave Mattis carte blanche publically.. and Mattis sleep walked the US to the point of having to endure what would have been a swift and excruciating date with reality.