Why or why not?
I've been thinking about this for at least the past four years, and I have recently decided that I don't think it's in the best long-term interests of the U.S. to engage the PRC (People's Republic of China) militarily. So no, the U.S. shouldn't provide military to Taiwan if China attacks them.
Why? Because there is a very good chance that China will become our biggest competitor for resources over the next 50 years. The last thing we need is an economic competitor who is also a military enemy. While this still leaves the question of democracy on Taiwan up in the air, I also think that the PRC is slowly becoming more free on its own. Maybe not as quickly as we'd like, but it is happening. But if we face off militarily, it would stir up their nationalism so much that it could stop or even reverse their slow march toward a more democratic and open rule. There are times when military force is required, but I don't think that the "Taiwan case" is such a time.