You can though - at least to the extent that we in empirical science usually refer to "proving" or "disproving" (or rather, indicate or contraindicate a hypothesis). In this case it'd be studies/metastudies on injuries in different kinds of matchups (which can either show a statistically significant difference or not) or in performance of different athletes.
Yes, and I'm sure (especially for boxing) there are more injuries. I'm not trying to argue against that. I'm saying, it isn't worth the witch hunt. Iif you care about injuries caused by trans athletes, are there actually a large enough number to warrant this. Presumably we shouldn't be preventing cis-women from competing, even if they cause more injuries, right? It's boxing. Injuries are going to happen. If there are cis-women who just hit really hard for some reason, that's part of the sport.
The case you linked here is regarding football, not boxing, which simply makes it a question of performance rather than also safety (as it is with boxing or other combat sports).
Exactly. Even when injuries aren't the issue they're pushing these rules, so I don't trust that this is particularly strongly inspired by injuries. It's about people complaining trans athletes (or rather people they, usually baselessly, suspect are trans) are ruining the sport for "real" women.
Performance wise, the most "fair" might be to sort athletes into leagues based on testosterone levels. It's already known that higher testosterone levels tend to correlate with higher performance, so rather than imposing an arbitrary limit where only the athletes in the "sweet spot" just below the limit get to excel, grade them into brackets based on that.
This has been my argument for ages, or at least it's the logical extension of the argument that we should be protecting women in sports by banning certain women who we don't want competing. The fact of the matter is high level sports selectively choose certain attributes. I'm sure as hell not a top athlete and could never be. I'm not asking for rules to be made that allow me to compete against top athletes, but if we need to protect women's "fair" competition strongly for some reason, shouldn't we also have leagues for all types of people? Doesn't longer arms lead to more injuries in boxing? Is it "fair" that sports aren't designed specifically for me to be able to win?
I don't know what the answer is, but breaking sports into a "premier" league (no barriers; anyone can compete so only the best of the best rise) and then having a ton of leagues with different sets of rules to exclude people seems like the logical conclusion to this. I can't honestly say I think that's the best solution, because it'd make it ridiculously hard to watch, find teams, and track. I do think it's the only way the argument for testosterone testing works though. It doesn't work if you're excluding cis women from women's sports, otherwise it isn't actually protecting the integrity of women's sports. Top level competition is a game of outliers.