Okay, first I'll start with what you did wrong. When you said you pushed in then pulled out on the axle, you must have done that with the actual shaft (round bar) itself, which caused it to pull out of the boot. With that said, I see a problem that must have been from the factory. There should have been a tri shaped roller bearing assembly that rides inside the section that is still in the trans. It is held onto the end of the shaft with a clip, which must be missing or broken and the reason it pulled out like it did. It would have still come apart, but it would have stayed in the boot, because you wouldn't have been able to pull it through the boot hole. Now, how you should have done it. You should have removed the axle nut on the other end of the shaft and then pushed that end through the hub assembly. That way the axle stays with the machine. If I recall when I did my bushings, I used an impact gun to take the nut off, but you can also use a long breaker bar. At this point, if it was me, I would just replace the axle with a new one. You can put your old one back together, but you'll need a boot kit, which along with a boot, would come with a packet of grease and new boot clamp. You would also need a new clip to replace the one that's missing or broken. You'll still have to remove the end of the cv axle in the trans, which can be difficult to remove. There should be plenty of threads on that subject if you put in a search. Just remember, shit happens and not all lessons are free. 😀