I think that one perspective is that while we may believe that we're acting out of compassion when we use euthanasia, it requires a deeper look. All beings want form, and they want to exist.
I have a daughter and I gave her life. Even if she became very ill and was in terrible pain, I can't give her death. Life, but not death. Dixie, my sweet furry friend, could not be given death by me either. Her pain during her last days broke my heart, literally. It was so terrible and hurtful. But compassion to me meant trying to help her tolerate the pain medicine and providing her as much comfort and love as humanly possible.
But her death was not up to me. It would have ended my suffering to give her a trip to the bardo. But I'm I don't have the wisdom of a Buddha, I don't know Dixie the dog's mind. I don't know how she felt about her own impending death. I feel certain she knew. All I could do was love her.
My furry little one was a member of the family. I treated her as such.
Sometimes we think we're helping others with suffering but if we step back, we may be addressing our own pain and suffering when we see loved ones in pain. And dying. We need to sort that out, and figure out what's us and what's them.
Beings want to live as long as they can, it's what all samsaric beings crave. Existence. It just wasn't up to me to make the choice about her ceasing to exist in that form.
Whether it's a human, a cat, a dog, or a beetle, I can't intentionally take life. It's not for me anymore, no matter the circumstances. That's why the Buddha kindly gave us the first precept, because we're ordinary still, without the wisdom of an enlightened being.
People still need to do what they need to do. I know this. I'm just offering a perspective