Euthanasia as in animals, no matter the quality of life, adoptability, and years left, are put down by the thousands because they're inconvenient to keep alive and get adopted while PETA preaches that killing animals is wrong. Also, did you read the bit about them kidnapping animals from kids and old people?

Plus they're cowards without the courage of their convictions. When I was growing up their protests included throwing red paint on people in fur but they wouldn't do it to someone in biker leathers. One got them shunned and laughed at, the other would get them killed like the animals they stole.

TL;DR their whole schtick is to either destroy others' property or steal loved members of families who have fur while killing many more animals than they save.

It's not mercy killing when the animals weren't suffering and weren't voluntarily given up. It's murder for the sake of their agenda.