They are against breeding animals for the purpose of owning them as pets. It's a tough pill to swallow as an animal lover who enjoys living with animal companions, but I have to grudgingly accept that they are right. It's unlikely to be a real issue in our lifetime since there are so many shelter animals that can be adopted though. They certainly don't believe animals are better off dead than pets, I don't think you'll find anything credible to back that up. From what I've read, their kill rate is so high because they only take in animals that other shelters won't. The "no-kill" shelters even send their unadoptable animals to Peta to do their dirty work.

They're abolitionists, not just animal welfare activists.

Are you saying you think it's ok to unnecessarily kill animals as long as you treat them well beforehand?