If they're using a false term but quoting someone they should use quotes:

Xi warned Biden during summit that Beijing will "reunify" Taiwan with China

The nation wasn't developed by the people who escaped. That's an ahistorical way of framing the issue

Taiwan was developed by the overthrown proto-fascist military junta who just lost the civil war. After taking the island, they didn't tell the people of Taiwan that the war had been over and they were no longer China until 1991. The first labor laws outlawing slavery were introduced to the people of Taiwan in 2006. The people of Taiwan still consider themselves China (it is afterall the name they go by, not Taiwan) and full Taiwanese independence is still a minority held belief on the actual island.

Just to be clear, I am a supporter of their independence, but this is a very messy situation in which the political party who comrade the country is the same fascist party who lost the war in the first place and still maintains to the UN that they are the legitimate government of the mainland. Full separation is convenient for the West, but neither side actually wants that, they just don't want to be ruled by either fascists or communists, and I think that is incredibly fair for all people actually involved to want.

Even before that Taiwan did not belong to the rest of China.

There were some settlers from the main land, but the indigenous population always controlled most of the island and the Chinese settlers were careful not to antagonize them.

This lasted for hundreds of years, pretty much until a brief period at the end of the 19th century when the Chinese government decided to send troops to brutally subjugate the indigenous population, only to shortly after lose control of Taiwan to the Japanese.

It's a historical fact but how is it a tautology? Territory can change hands during a civil war as evidenced by the RoC no longer controlling China. Unless I'm misunderstanding something. Either way I don't think that changes the point, if that's a tautology then claiming that it can be reunified is a contradiction.

Militarily speaking, the situation is similar to Cuba and US during the Cold War. Taking control of the island will grant them more military security.

I don't really know if that makes a whole bunch of sense..... The only country with the capabilities of attacking China is the US. The only real provocation that may spark that military conflict is an attack on Taiwan or South Korea.

Taiwan isn't even that advantageous of a location for an invasion either way, the strait of Formosa would be a death trap for any amphibious landing. The most militarily important region for China is and always has been the Korean peninsula.

I think Chinas main motivation is that Taiwan disrupts their plans to completely control trade routes in the South China sea. Once the 9 dash line is under control and expanded to include the territorial waters of Taiwan, China will have a defacto monopoly on trade for most of eastern Asia.

True but that doesn't work too well to invade an island.

China's big problem is what they offer internationally is cheap labor and they're going through a population collapse now, like other countries that ascend economically, people have fewer kids and younger workers want better salaries and conditions, (understandably so!) This combined with the US's trade war with them has caused international companies to move a lot of production to other impoverished nations like Bangladesh, Vietnam, and Mexico, among others instead of to China. China's economic miracle was because of this large pool of population that is vanishing. Sacrificing soldiers of reproductive age would accelerate this problem.

Glory to Taiwan and their West Taiwan acquisition project!

The problem is that any such reunification would presumably be on the PRC's terms, and that didn't turn out so well for Hong Kong.