non pedigrees are healthierAs has been mentioned, there have now been several times that research was carried out and proved there was no difference. Before the most current one there was the one the RSPCA paid for, presumably in order to prove pedigree dogs were unhealthier, which showed there was no difference.
we have far to many animals in rescue to be breedingIf I wanted a dog, or cat, I want to know that I get the temperament I'm looking for as well as a healthy animal that has every chance of living a long, happy life. I don't want an animal that may well have behaviour problems and hidden illnesses that will only show up in a year or two. I'd be happy to give a home to a rescue, and have done many times, but then it will be understood that it may not work out.
For novices and/or families with young children it's especially important to know what you're letting into your lives.
we don't need pedigrees there are plenty to go roundBut we do. There's reasons given above but there are a lot more: How would we get police dogs, guide dogs, sheepdogs for instance? Yes on occasion a crossbreed or mongrel may suit the purpose but if it really was as easy as taking any randomly bred dog and train it for these jobs, why don't we see mongrels working in them? How would we know that the mongrel is going to herd the sheep rather than killing them, or would help the police catch criminals rather than make friends with them? Breeds are born with natural abilities as they have been deliberately bred for, often for hundreds of years. That's why a Golden Retriever will carry things around, why a Border Collie will try to herd and a German Shepherd will guard, regarless of whether they have had any training for it or not.
Pedigrees are man made and we continually alter for our pleasureThat's true but it's also true of for instance cows, pigs, sheep and chickens. With those they are altered because they are wanted as food. Be bigger, grow faster etc. Is it more acceptable to create an animal that will be eaten than one that will be a pet or a working animal? What about horse breeds? Rabbits? There are so many pedigree animals in the world, far from just dogs and cats. Even fancy mice are extremely different in body shape and size and colour (and on occasion coat) to wild mice.
Cats: the same arguments applies with the exception of working roles. You get a pedigree cat and you will have a very good idea of what its temperament will be like. With moggies you can have some idea based on the colour as temperament is very much colour related, but you can't be sure. I know I couldn't live with a Siamese, for example. I like calm cats.
Back in February I lost my most special cat, a Persian who was 17.5 years old. He was very much a lap cat and he even responded to commands, like down, go to your bed etc. This summer I got a new kitten, as did two of my children with my grandchildren. We all got pedigree cats. I acquired a Maine Coon, a dog-like breed who isn't as calm as a Persian but who still likes to sit on my lap. My daughter who has 4 children got a Ragdoll, a breed known to be laid back. My son who has one child got a British Shorthair, also a breed known to be fairly calm. I adore my Maine Coon and his best friend is one of my Papillons -they play together just like dogs. But he isn't as easy to handle as my Persian was. He's huge and strong and if he doesn't want to do something he will complain. My grandchildren can say hello to him, touch him, but they cannot pick him up as he doesn't like it and will scratch. Their Ragdoll however they carry around a lot and he happily accepts it. He plays with them, sleeps with them, and you never see his claws. Just like you'd expect from this breed. The British I haven't met yet.
Finally, pedigree cats are bred to be indoor cats, or the great majority are. They are happy to live as indoor pets. My rescued moggy is forever trying to get out. If you live where it isn't safe to let cats roam (and I dare say most places are not) then a pedigree cat is a better choice.