Lyric discussion by Blithium 

Cover art for Broom People lyrics by Mountain Goats, The

I think that the 'wild creature' line is both an expression of his freedom while he's with the girl, and a retaliation against his stepfather's violent oppression. Kind of like saying 'You've pinned me down, I've got back up, and now I've got you, and SHE'S got whatever's left of me to get.'