I don't see how responsibility and being a "real man" (whatever that is) has anything to do with masculinity. A responsible person is a responsible person is a responsible person.
Your use of man up and pussy are exactly my point though. It is inferring that if you accept your responsibilities, you are called a man, while if you are irresponsible, you are "bad," a pussy, ie. a woman. You probably don't think of it this way, and you probably don't even agree to the sentence that the language infers to, but that's just because people don't all necessarily think of what the language that they're actually using infers, since it is so common. But whether or not someone agrees with it, this is what is being acknowledged (on some level) when such language is used.
Well... Really... "Pussy" refers to a cat so....
Im not talking about how masculine you are physically, I'm talking about guys who need to man up and not be pussies when it comes to real issues.