The US is using Taiwan as a balance against Communist China, threatening at least to intervene militarily if China ever makes any moves on Taiwan. There are a number of possible reasons for this.

1) Goodwill for the Taiwanese people, in the case of foreign attack.

This is pretty dubious, because the only reason Taiwan is making provocative moves in the first place is US support. If the US makes it absolutely clear that it won't defend Taiwan, there won't be such a war in the first place.

Besides, color me skeptical of any US-goodwill-in-the-world argument.

2) Part of a containment policy, analogous to the one that brought down the Soviet Union.

Except that such a policy doesn't exist. China isn't going to up and collapse, like the former USSR. If the US were really interested in this outcome, it would have had to challenge Chinese moves into Africa and South America decades ago. If Taiwan is part of a 'container,' it's perhaps the lid, missing the body.

3) Part of a carrot-and-stick policy, related to issues of common interest (China's relations with autocrats in the Muslim world; North Korea)

Except that a stick cannot exist without the corresponding carrot, any more than that "one hand clapping" koan. I don't see any evidence that China, or even American lawmakers, see any connection between those two issues.

4) To make profit off of arms sales to Taiwan

Now we're getting warmer. Still, I suspect the real reason is

5) Just to piss China off. AFAICT, this is considered a legitimate foreign policy goal in its own right by the US public and policy-makers - and in the left just as much as the right. It's usually much easier to use China as an election-year issue than to make genuine attempts at working out cultural differences.

To be clear, I wouldn't say the US should exit the region tommorow - any sudden moves would clearly be desabilizing. But this should be long-term goal of the US.