Ive heard about this quite a long time ago. They seem to believe that these animals are better off dead than with people. They dont really seem to support keeping pets and do not support no-kill shelters, which do not euthanize animals generally but keep them until they are adopted.
PETA says they want to help animals but they dont seem to do much to actually help them. From reading over the whole article it seems they do not care about the animals at all, do not try to even adopt them out and find them homes and seem to only be interested in killing them. They're actually applauding and encouraging the killing and this was pretty disturbing to read.