Let’s get the bad news out of the way first: You can no longer change pet specializations. Each pet family is locked to one of the 3 specializations. Mechanicals will always be Cunning, Ravagers will always be Ferocity, and — most peculiar of them all — Spirit Beasts will always be Tenacity. Those are just 3 examples, you can see the full list at Wowhead.
For the most part, the assigned specs of each family make sense, but I have no idea why they are doing this now. We’ve been able to change pet specs for over 5 years. Why take away this customization now? Was there something so terrible about a Hunter wanting to use a Ferocity Turtle?
The response to this has not been pretty, but I do think part of the uproar is because people think Ferocity pets will still do more damage than a Tenacity or Cunning pet. This no longer seems to be the case.
Update: Blizzard has made a post clarifying the new system.