They can’t prove anything. It wasn’t until fairly recently that courts, law enforcement agencies, and prisons recorded statistics on gender identity, most of them *still* don’t, and some of the ones which do don’t do so reliably. So there’s not nearly enough data to serve as a useful comparison. Anecdotally it appears that the majority of trans women arrested for crimes are arrested for prostitution and/or drug use, both of which seem to have gone down since increased availability of gender-related care and the cessation of the war on drugs. Usual caveats about anecdotes, of course.
As for the semi-well-known newsworthy examples, there are what, six? There’s Isla Bryson, the rapist (who is currently being moved to a men’s prison, ugh), Tara Wolf, the pro kickboxer who delivered a beatdown to a Karen (physical assault), Hannah Tubbs, the child molester (who was a minor herself at the time but charged as an adult), the Wi Spa Incident, which was “definitely some trans woman” but turned out to be a cis man and serial flasher named Darren Merager, and at least two trans women who exposed their breasts in public (one of which was severely drunk and topless in a hotel pool, the other of which pulled a “does this look like a man to you” stunt in response to repeated misgendering), I don’t remember their names. And that’s over the past decade or so, not just last year or something. Not exactly an extensive list, and only the first three are actual examples of a “trans woman/girl being dangerous to other people”.
But of course they don’t need proof, because men do things like that all the time, so “obviously” trans women do it all the time too. [Narrator: It is not obviously happening.]
[EDIIIIT] Dammit, I can’t believe I forgot the most famous one: Chelsea Manning, the whistleblower convicted of espionage. So 7. Or maybe not, because that was well over a decade ago (2009).