On the surface, shooting them down seems like the best idea, but that's now we know what happened, and without thinking about it as it would have been at the time.
Until they know for sure that there's no way the hijackers are after anything, there's no way you can negotiate with them etc,then shooting it down is basically killing your own citizens.
And then there's obviously where the plane hits after you've shot it down, and I'm guessing the debris from an airliner traveling at that speed would cover a pretty wide area. Heading towards New York, it would undoubtedly have landed in some suburban area with shchools and houses
Plus it was, what, fifteen minutes (?) after the first plane hit the first tower that the second one hit. So it's only in that time frame that you know for sure what's gonna happen and you have to make that decision. That's not long, and the plane's likely gonna land in a densely populated area. So you're fucked either way then.