The way I learned was that if an attack is pushing, then pull (step backwards) and if an attack is pulling, then push (enter in).
I thought that this was the way of Aikido and I'm supprised to read that so many styles do not step backwards.
Entering is not the same as pushing. Moving a foot back is not the same as pulling. In aikido you're generally trying to get to their side.
It's one of the main technical differences between the two.