Correct me if I'm wrong, bagface, but reading this thread I get the impression that you are afraid that your girlfriend will be "brainwashed" by this magazine and makes her to want you to turn into what Cosmo describes as what a "man" is supposed to be.
And that you can't live up to that image of what Cosmo describes and that she will eventually will break up with you.
And that that's the reason why you want her to stop reading it.
Well, maybe I'm rambling a bit here, but that's what it looks to me.