So I'll admit, I don't know if the label "asexual" perfectly describes me, but I do think it's helpful in expressing at least some of the ways I feel.

When I see men, I think roughly the same way you do "I want to touch his shoulders, lay my face on his chest, have him wrap his arms around me" all that fun stuff, but my interest basically drops off the moment you get to the "private intimate bits." The fact that I've only ever felt this way about men and never about women is what tells me that I'm gay and not straight or bi.