In my opinion, every animal should only be bred if it will be an improvement on it's parents. I don't care how cute or sweet it is. If you don't show to prove their qualities, then you need to be well versed in proper breed standard, be it a dog, mouse, horse, or snuffalaffugus.
All dogs to be bred should be within breed standard, have an excellent temperment, and have the proper testings with acceptable results. Different breeds need different tests including eyes, hips, ears, thyroid, etc.
For most occasions, a person will not own both parents of an animal. What are the odds your bitch/mare/doe perfectly matches your stud/buck/dog? I have greater respect for a owner who searches for the correct sire then just uses the most convenient one.
With the exception of horses, I don't think mutts should be bred. What's the point? Go to a shelter, there are many EXCELLENT choices, purebred and mixes.
If you don't have a specific breed of cat who is well bred, don't breed. There are kitty mutts of every size, shape. Color, and fur in shelters being euthanised daily.
No pet shop animal should be bred. They are bred for a profit nothing else. The health, temperment and conformation of the dog are not taken into consideration.
I have no problem with people who breed for example mice for snakes. BUT they should have proper equipment, be knowledgable about the healthiest food (you are what you eat) and should have a customer base. I don't like people who say "I'll just breed them and give them to whoever, someone will take them". I don't have a problem with people who say "these mice are being bred for consumption. I have proper euthanasia equipment and freezing equipment. I have means for developing a client base and will not produce more then will be purchased or used for my own reptiles"
A well bred horse is one exception, but for 99% percent of animals, you will be losing money if you breed them correctly. Vaccinations, health tests, finding a stud, and showing are costly and time consuming. I prefer to think of it as an expensive hobby, not a career
I could go on for hours, but I will be good and stop here