Taiwan is actually very close to two very important US allies, the Philippines and Japan. It’s alot harder and more expensive to launch an attack from Luzon or Okinawa than it is to launch it from Taiwan.
FWIIW it was historically used by forces which threatened Chinese sovereignty, including Japan. Since Chinese leadership actually reads history instead of making stuff up as they go along, as Westerners do, that's probably why it's such a sore spot for them.