Remember, you have to pull the bearing by applying the force to the same ring (inner or outer) that is resisting the motion. So, you pull bearings off a shaft by pulling on the inner ring, and you pull them out of a housing by pulling on the outer ring. If you pull on the wrong ring, you will Brinnel both of the bearing rings and it may have a very short life afterwards. Of course this doesn't apply if you know you are going to throw the bearing away after removal (but you only know that if you have a new one already to hand - we've all had to put second-hand bearings back in when it turned out the type had been discontinued and was no longer available). You usually need a split-ring of suitable diameter to pull bearings off a shaft without damage. Pulling them out of a housing is even more difficult: fortunately they are seldom a tight fit in housings.
Same rule applies when installing the new bearings: drive on the outer ring to install in a housing, and drive on the inner ring to install on a shaft. It is good practice to use a suitably-sized piece of mild steel tube between the hammer and the bearing ring. Hard-against-hard equals chipped part.
