PETA and all its warranted and unwarranted baggage aside, this seems to be a difference of opinion on whether we have too many domestic animals or not and whether it's better for the animals to have fewer numbers so that fewer of them will end up abused, homeless, etc.
PETA seems to think that overpopulation is a big problem since lots of pets end up having to be euthanized because no one will take care of them. There is a good argument in this, that there are more pets than people wanting to take care of them. PETA, I believe, is in agreement with most people in thinking that the solution to the problem is spaying and neutering pets. I guess they're just willing to act more decisively about it since they believe that conditions aren't always going to be good for the animals and that in lots of cases it's better overall for some animals to be euthanized.
I dunno. I like the idea of no-kill policies, but I can sort of sympathize with someone who thinks the problem is so big that it can't be ever managed without drastic measures. I'd never be able to bring myself to do what they're doing, but I can at least understand where they're coming from.