Well it isn't like they're individual species, they're just a subset of a species artificially created by humans via selective breeding. I don't oppose them in general tbh... if people want a type of cat or dog then why not?
I could however see an argument for ending some breeds or trying to change some behaviours among breeders - like when it is damaging for the dog for example - Pugs and similar dogs prone to breathing issues, German Shepherds bred with the silly sloping back prone to issues etc.. Those things ought to be changed/modified and not encouraged.
Also I don't see much point in say carrying on breeding fighting dogs - pit bulls/bull terriers (technically I guess pitbulls are illegal anyway but ill defined) - I'm not advocating taking away people's dogs but rather just neutering them I just think that general type shouldn't exist anymore in part because of a subset of owners and in part because of the disproportionate jaw strength and amount of damage they can do if/when they attack... any dog can attack and some breeds are more aggressive than others but an aggressive small dog that can't do any damage isn't really as big a deal.
Yeah I won't disagree with some of that.
Sphinx cats or dogs with really short legs, or any breed notorious for health issues. Really short noses, breathing difficulties, etc. There are some breeds which simply exist to perpetuate what you might otherwise regard as a disability.
But more generally, humans have been breeding animals, and in doing so manipulating their characteristics, since time immemorial. I don't think there's any desire to stop it, except on grounds of animal welfare or breeding dangerous animals, etc.
There's nothing inherently wrong with having registered animal breeds, and indeed many breeders have made extensive efforts to outcross their breeds to improve the general health of the breed.
I'm fine with really extensive controls on breeding, mandatory registration and any measure designed to protect animal welfare. Absolutely in favour of measures to ensure or improve animal welfare. And also efforts to cut out the clowns (who exist in every industry ever conceived).
But I wouldn't say animal breeding is inherently "wrong" as some have come close to suggesting in this thread.