The point is that saying "Some statements come with institutional power behind them, others don't." doesn't somehow magically erase a problem.
Institutional power is only a single aspect and not the only factor in whether or not saying something shitty is harmful.
I have seen this way of reasoning a lot when it comes to female on male abuse/rape where it's used to derail the discussion into "but women still have it worse so male victims don't count". Maybe I'm just a bit too used to this way of arguing so I overreacted. But it seriously pisses me off.