mini/micro/teacup pigs are not a breed, the breeders breed from the runt of the litter to keep them small. I do not agree with this, this is interfeering with nature.
Whilst I agree with your sentiments, it has to be said that any breeding of animals where natural selection is denied is interfering with nature. It's only when breeders have little or no idea of genetics and sensible breeding practice that problems occur. I am not suggesting that the OP falls into that category.
Most breeds of domesticated animals are selectively bred for specific traits which are desirable to us, and line breeding and, at times, in-breeding, are the means by which developments are made. Yet many people recoil in horror if one suggests using two closely-related individuals in a breeding programme.
All the poultry breeds have been developed using line-breeding techniques, yet people still believe they can improve on their stock by consistently using unrelated stock. Line-breeding and occasional in-breeding, with timely use of a suitable outcross, is what fixes desirable points in a breed. The problems occur when undesirable points are perpetuated in a breed, and this can be caused by ignorance, or bad choice of stock, or just plain bad luck.
Good breeding is not just about producing perfect babies; it requires a critical breeder and much culling or, at the very least, the non-inclusion of certain individuals from the breeding pool.