For the China part: Yes, the "by force" part certainly exists as a position, in competition to the peaceful unification approach. It's important to keep in mind, though, that the confrontative position of the first Trump administration and afterwards the Biden administration significantly helped the "by force" faction. There was an interesting piece in Foreign Policy about that, a social scientist from the US was questioning Chinese students at an elite university on this very topic and thus had the chance to do a time series observing the attitude change following US actions.
Secondly, in Taiwanese politics, Unification is actually a big topic and even has its own party, the New Party, advocating for it (plus the fringe CUPP). Not popular right now, but certainly existing - and evidently falsifying the notion that the all of "Taiwan doesn't want to be part of Beijing's China".
So according to your logic, it only counts if it's unanimous inside Taiwan to not be taken over by Beijing but it doesn't need to be unanimous for those who want reunification with China?
No. I pointed out that both the "by force" statement for China and the "Taiwan doesn't want" statement are so oversimplified that they became factually incorrect. The "logic" is your inference and neither stated nor implied by me.
The existance of a faction within Taiwan that wants Taiwan to reunify with Beijing's China isn't materially relevant if they don't have any path forward to accomplish their goal.
This is about international relations. You won't get any insight into it if you reduce any point you don't like to argumentative metaphors.
Even within the framework of (structural) realism so popular in contemporary US politics there's this well-known problem that the buildup of defense capabilities of party A looks like aggression to party B - and vice versa. See the seminal work Perception and Misperception in International Politics. Or the relations of Britain and Germany before WW1 and WW2.
The FP article I mentioned, "Trump’s Trade War May Make Elite Young Chinese More Nationalistic" [1], illustrates the argument. You have actual empirical data, changing over time, after exposure to the "treatment". So at least a hint of causality.
No no, I mean that one does not conduct foreign relations with fear that your approach might give fuel to the local autocracy to whip up fabricated nationalist riots.
