PETA does actually put quite a few animals to sleep. Their purchase records are on public record, where you can find industrial freezers and euthanizing agents. When they go out and firebomb a humane society's director's house, it doesn't occur to them that the fact is that there are way too many animals and not enough homes. They aren't an organization set up to adopt animals out. A shelter situation isn't really possible, and those animals have to go somewhere. Something like 75% of the animals in PETA's custody are euthanized. (I don't know the exact figure off the top of my head, but I can look it up if anyone needs to know.) They think they're doing the animals some great favor by "liberating" them, when everything they do just makes other animal rights groups look bad.
I'll give an example. Near our home in Wisconsin several years back, there was a story in the paper about PETA activists breaking into a mink farm at night and releasing all the minks into the wild. (They were destined to be fur coats.) Well, these were farm minks, and therefore had never seen "the wild", and had no idea what to do in it. The vast majority of them were killed on a nearby highway. The rest were picked up by other predators and probably made a pretty easy meal. Now what kind of moron doesn't think something like that through?
There are other problems with PETA, such as their advocation of violent crime in the pursuit of their goal. The director of PETA was quoted calling one of her seasoned arsonists a "fine young man". This kid had been convicted of arson and assault several times. When he wasn't in jail, he was holding seminars on how to make small bombs, break into buildings, and set fires. (Apparently he didn't know how to set fires well, since he kept getting caught.) If it was up to this organization, there would be no animal research or even pets. No dogs for any of us if they had their way. They're strongly opposed to medical research on animals, but several of the "higher-ups" in the organization have long-term medical conditions that they treat daily with medicines that came from animal testing. One even has had an organ transplant, which was first performed successfully on a chimp.
You guys all know how nuts I am about animal rights. But there are ways to do things intelligently and ways to do things that make you look like an idiot. PETA practices the latter. Breaking into buildings and burning down the homes of humane society employees accomplishes very little in the grand scheme of the animal rights movement. What it does do is make the entire animal rights community look crazy. There are a TON of other organizations that are actually working hard in and with the system to win more and more protection for animals. PETA's not one of them.