Toxic masculinity isn't quite the same as "too masculine", it refers to some traits that are often assosiated with men/manliness that can be more or less harmful when much of society has that mindset and how bad it is how common, accepted and/or even EXPECTED those traits are from men (by other men and sometimes women too). For example, how many men think that they need to and (maybe even worse) that it's OK to defend their honor/whatever with violence. So if someone says "fuck you, asshole!" to them or maybe their child or partner, the first and only appropriate & acceptable answer for some men is to start a fight and beat the person up. Because that's what a Man does. They don't talk, they don't ignore pathetic insults thrown at them, they don't try to de-escalate the situation to avoid fighting and just move on in their life, they "let their fists do the talking" the second someone is disrespectful of them and a lot of people would just cheer on when that happens. That is toxic masculinity.
Now, I haven't seen BvsS so I can't really say if there is toxic masculinity in it or not or what kind if there is, but comics do suffer quite a lot of toxic masculinity, much like they do of sexist portrayals of women, so it wouldn't surprise me if Battie vs Supes had some toxic masculinity problems (especially considering the director's past work, he's not exactly the model example of someone who understands gender issues).