I refuse to let us get a cat from a breeder.
What's wrong with getting a cat from a breeder? Do you think they are less healthy?
Because the only difference between that and a street cat is that it has papers.
A pet is a big decision and you are allowed to get the pet you want from where you want. If you can't or don't want a cat from a breeder it is okay to get one from a shelter. You don't want to resent the pet after paying too much.
Maybe I could just not get a pet at all.
If you don't want to get a pet, that's also perfectly fine! Pets are a big responsibility and require a lot of attention to properly take care of. Make sure to think it over before signing up for that much responsibility.