The term Avril Push was derived from Avril Lavigne music videos which, more or less, follow the same formula. Theres always a man that looks like hes from a shampoo/hair product commercial that is mean to Avril. At some point in the video, Avril pushes this man away from her (almost always in slow-motion) and then runs off to sing into the camera.
This term has come to describe any scenario in which a distressed woman pushes a man away in an overly-dramatic fashion and then runs off.
Angus: "Yeah so what happened with your girlfriend last night. You were at the party and she was acting like you were being all mean to her. Did she Avril Push you?"
Roger: "Yeah, it was weird. I was talking to her and then she pushed me really really slowly and then ran away and started singing."