[embee]

You really need to press/pull the bearing into the housings by applying force to the outer race not the inner. Note the tool shown uses old bearings against the new ones but also full diameter sturdy "washers" so the force goes through the outer race and keeps all the surfaces flat together so when it reaches the spacer it will stop.

If you use the spindle and pull against the inner, it puts all the load through the balls and can indent the races at worst. Because of clearances and flexibility, you will always end up with the outer race not pulled in quite far enough so there will always be a lot of side load on the ball bearing when you then tighten the spindle. This will seriously reduce the life of the bearings so you'll be back to square one very quickly.

Note similarly if you press the outer race only, without the flat washer across the inner also, you can end up in a similar situation but with the outer race too far in and thus loading the bearings up in the other direction.