Again, did you ask where was America when the refugees were pouring out of that country looking for a safe haven ? We could have certain absorbed as many of them as any of the nations that took them in. But America stood by and let that burden fall on them and they took that load as their part in the effort.
As far as Obama goes his term ended. But it did end with him pledging this nation would not abandon the Kurds. The military leaders on into the Trump administration stood by that pledge, pleaded with Trump to stand by it as well, and then quit when they realized Trump was going to go back on it.
The safeguarding of the troops was being done by the might of the US military backing them up and America's political power to pursued the rest of the world to follow it. Trump chose to have the US military retreat in the face the Turkish military and he then even cancelled sanctions the day after imposing them. Making a mockery of any claim to political power in regards to the situation in Syria.
As to why the US should take the leading role in the world's affairs. The last time we sat back and just watched this guy in German with a funny mustache decided he should be the one to do it.