He does display more than those traditionally masculine traits. He portrays himself as a protector of the vulnerable and a provider. Making sure women and children are safe and provided for is very traditionally masculine. He has made it a point of his political career to help children, and as an ex-member of the national guard, he can claim that "protector" archetype.

This is not to say that there aren't problems with traditional masculinity, but there's more to it than just family.