No, this isn't an idiom in English.
All doorways can be walked through from 2 directions. If the door only turns one way ("opens inward" or "opens outward") then it is a door you "push" from one side, and "pull" from the other side (using the knob or handle). There are a few doors, often in restaurants, that you can "push" in either direction. But we don't call them "push doors".
A locked door can't be opened by pushing. It must be unlocked, or opened from the inside. So in your example it was unlocked, but the person didn't get in because he only tried pulling, not pushing. We would call this a "door that opens inward" (swings into the house when open).