Taiwan Issue

It's simple, both sides are Chinese, no doubt with that, both sides had claimed there was only One China, and each claimed itself to be the only rightful representative, the problem is, the smaller one had, or has good relationship with the most powerful country and hence with the Europe, and became prosperous, and democratic. There was a time that each side wanted to conquer the opposite, but after the 90s, it became unrealistic for the smaller one,  so it wanted to claim it's not China, claim that it's a different country, more "evolved", at least more connected to the world that led by the Western group. The bigger one finally became strong enough to conquer the island, but that would sabotage the interest of the United States, undermine its global influences, which U.S. would not let it happen.

Basically it's a matter between the Chinese, but the United States wants his cut, which the PRC would not give, period.