No that's not how it works, and you are mixing things up here. Toxic behaviour does go deeper, but here it repurposes standard stereotypes as a way to regulate gender relations. It is not the act of being masculine in itself that is a problem.
But using gender in a way that ostracize and encourages violence absolutely exists and is definitely toxic. It just happens to target men more as it pushes them to gain back power and authority. Having an accurate and specific term for the problem makes sense.