Most pets can be equipped and trained by any wizard, but there are some that are school exclusive. These are generally given as quest rewards. In the past, it was impossible to obtain a pet you couldn't equip, but that was changed in an update a couple years ago. IMO this was a TERRIBLE change, as now you can waste gold getting an unusable pet.
I wish KI would restore to the original hatching restriction, or at least add a warning when you try to get a "wrong school" pet.
