Does gravity push or pull?
This simple answer is that gravity is only ever observed to be an attractive force. Unlike the electric force where charges can be both positive and negative and either attract or repel depending on the difference in charge, there is no such thing as negative mass. All massive objects attract each other. Gravity never acts to repel two objects.
The more complex answer is that it doesn't matter how you think of it. The formula for gravitational attraction depends on the mass of each object (
And the even deeper answer is that we don't know. Of the four known fundamental forces of nature, gravity is the one we know the least about.
Some scientists speculate that mass is simply a disruption of space and time. Deformations in space/time are massive objects. Waves in space/time are the motion of massive objects. Gravitational attraction is simply the tendency of massive objects to move "downhill" in this deformed space. You might think of the "hill" as pushing in a particular direction. And you may then ask, "Did the two objects pull each other? Or did the deformed space around the objects push them together?"