Like they do with unwanted pets, they’d slaughter the lot of them.

This is oft-repeated anti-vegan propaganda, but it doesn’t tell the whole story. I’m sure I could have a prebaked, lengthy response for this if I wanted, but I’ll try to give you the bullet points (sources on request):

• PETA is entirely open about its euthanization at their Virginia shelter. (Note: Do not click on that link unless you want to see some serious shit.)
• The rate is so high because they take animals absolutely nobody else will. This especially includes so-called “unadoptable” animals that “no-kill” shelters can’t keep but don’t want to euthanize to preserve their squeeky-clean, bullshit, artificial “no-kill” status that makes them look good but doesn’t help the animals that need it. Unadoptable animals especially include the terminally ill as well as chronically, intractably, dangerously violent.
• They also provide free euthanization to pet owners, where most clinics would charge a fee that many pet owners cannot afford (and thus will simply let their pets suffer until they die “naturally”).
• Society creates this problem by adopting, not shopping shopping, not adopting (leading to excessive breeding), having extremely minimal protections for pets and requirements for pet ownership, failing to spay/neuter pets (a service PETA offers for free), treating pets as possessions (e.g. that you get somebody as a present), and so on in the ecosystem of an immensely profitable and deep-seated pet industry.
• However, they do legitimately try to adopt out the few animals that get brought to them who are able to be adopted.

TL;DR: PETA is not to blame for their rate of euthanization. Just because they take on the responsibility of the problem everyone around them created to ease the animals’ suffering doesn’t mean that they take on responsibility for creating the problem. The flak they get for this from animal agriculture propaganda is entirely created as a distraction to delegitimize vegans as evil, murderous monsters so omnivores don’t have to consider the unfathomable scale and depth of suffering they deliberately cause.