I have a spirit of nature pet at adult. (Hatched damp demon with earth walker to get) AND it hasn't opened ITS epic slot yet. So far, it has opened these:
it could have opened the slot at teen. You have the same chance to get any skill each time the pet levels up. If you have enough gold it is a lot faster to just raise pets up to adult and see if they learn useful skills. If it reaches adult and it has two skills you like then I would suggest raising it to ancient. If not, then breed the parents again.
If you can't get enough gold, then I guess you could raise each pet up to epic, it is free but time consuming. I mean raising from ancient to epic is just as much effort as raising from baby to ancient. 875exp vs 1000exp
