It's hard to say when it becomes ethical to put down a family pet. Killing an innocent, sentient creature obviously seems wrong on the surface, but when it's done to prevent inevitable suffering from illness or injury, sometimes it's the most humane option available. Letting seriously sick pets die natural deaths can just be cruel if it prolongs their pain unnecessarily. But I'm pretty sure that most of the abandoned pets PETA takes in every year aren't in the position where death is their most favorable option.
Yet the animal rights advocacy group continues to put down thousands upon thousands of dogs and cats every year--and the death toll is steadily rising. A total of 27,751 pets have been killed at the hands of PETA since 1998. The organization euthanized almost 2,000 pets in 2011 alone. They found homes for a grand total of 24 pets in the same year. The group that's supposed to be looking out for animal rights is killing pets a hundred times more quickly than they're saving them.
PETA has defended their actions by claiming that the pets they euthanize are too sick to be rehomed or otherwise unadoptable. But they haven't produced sufficient documentation on the condition of the animals they euthanize, so that claim is rather a shaky one. They do seem to feel pretty adamantly that death by injection is preferable to life in human custody; the group has campaigned against pet ownership, equating it to slavery. They seem to be under the impression that animals, even the domesticated ones, only live in human homes because they have no way to escape.
I don't know about your pets, but every cat and dog I've ever had the pleasure of sharing a home with has greatly preferred the domestic life, human company and all, to the great outdoors. Even if you're of the ultra-vegan persuasion that animal captivity is inherently cruel, it doesn't justify the poor conditions in which PETA keeps the animals it dooms for the needle. According to an investigation conducted by the Virginia Department of Agriculture and Consumer Services in 2010, the organization's "shelters" didn't even meet its own guidelines. The report also indicated that most animals taken in by PETA faced euthanasia within 24 hours of arriving at their facilities. That doesn't seem like enough time to determine whether a pet might be suitable for adoption or not. Looks like PETA is just running highly efficient death mills for the animals they capture. Ethical treatment? Not so much.