And at several points they have characters more or less say a woman makes them better men.
Yeah, that is one of the worst parts of toxic masculinity and DOES NOT make a good case as a refutation.
The idea that men can't act civilized, compassionate, loving, rational and affectionate unless it's to a woman/around a woman is the the essential problem of the movie in terms of a feminist reading.
It's even what resolves the central plot point of the film. A woman comes in to communicate Superman's feelings for him, so Batman can go save another woman. And earlier, the dream sequence implies that the only think that keeps Superman bound to his principles is lois staying alive, because if she's not around, hey why not be a fascistic murderous monster? Like, it's not established how she dies, and without context of what about her dying makes Superman turn evil, (as opposed to the Justice League alternate universe episode where there's more to superman turning bad than "Lois dies", even if that's a crux of it) it's just implied that the fact that he doesn't have a woman around to keep him moral, a 'better man', he just naturally becomes a monster, since apparently he doesn't hold any morals of his own without her. Combine this with the fact that whenever he seeks moral guidance from either his mom or Lois on what he should do, you have him entirely dependent on women for how to act.
It's an idea that makes women responsible for keeping the world moral while not having much in the way of power and agency to make that change, so their morals and beliefs can only be carried through men. No, men have a responsibility to look after their own moral compass.
I know that none of this is what BvS intends to communicate, but...well, that's toxic masculinity for you. People complain that Wonder Woman is tacked onto this movie, but I think it's a blessing in disguise. Because she's written in so clearly late, she stays out of the drama of Batman's and Superman's bullshit and is just there to kick ass and not act as a moral figure towards them. Other than the SW prequels, she's probably the clearest example of how lack of characterizations is better than bad characterization.