What do you mean by a push and why did you push him?
A push could mean gentle pushing back against someone inappropriately invading your space that doesn't really move them and is more an assertion of your space "Sorry.Do you mind." That kind of push is probably not abusive.
A push could mean a violent and aggressive shove with two hands that sends someone tumbling down the stairs. That kind of push is probably abusive.
I say probably because context may make a difference.
There are a whole range of pushes on a scale in between.
What kind of push are you talking about?
But on any view poking someone in the face is aggressive, abusive and unpleasant. Accompanied by verbal abuse then it is abusive.