I think the key is that you don't want to force the inner and outer race to move out of the same plane. If you're pressing the bearing onto an axle, you want the force to be on the inner race. If you put the force on the outer race, the inner race will lag behind (due to the friction between the inner race and axle), and you have the situation where the races are being forced to move out of the same plane. The outer race is then "pulling" on the inner race, possibly resulting in damage to the bearing.

If you're pressing the bearing into a hub, the situation is reversed. Putting pressure on the inner race will now cause the outer race to lag behind, due to the friction between the outer race and hub. This will force the races to move out of the same plane and possibly damage the bearing.

If you don't have the proper tools to do this, I strongly support using temperature appropriately (as described above) to shrink or expand the parts and make assembly easier. A heat gun applied to aluminum parts works great to expand them.