It's not that Taiwan claims China, it's that the Republic of China claims to be the legitimate government of both Taiwan & Mainland China. Taiwan is just the 23rd province. The People's Republic of China (Mainland China) thinks the same way. However, taking back the mainland isn't a major initiative for the Taiwanese government.

Taiwan is pretty well defended and it's a strong ally of the United States, despite the fact that the United States does not officially recognize it. The United States sells Taiwan weapons and had a strong response to PRC military exercises in the Taiwan Strait in 1996.

Hi OP. There's nothing wrong with your question, but you've posted it in the wrong sub. /r/AskHistorians restricts discussion to historical events only, not current events, the latter being anything within the last 20 years. As such, I've removed this post; you might try x-posting to a sub specializing in Chinese/Taiwanese politics & current affairs, where there should be more specialists available to comment.