Why we don't euthanize humans:
In an extremely oversimplified, easy answer: Value.
Animals do not & should never have the same value as a human.
The premise is easy to see in the example of say, grandpa that is suffering from terminal lung cancer, who has been circling the drain and is dying in agony...or a trauma patient, bleeding to certain death in fear gripped hell - neither cannot be viewed as having a lower value than a domesticated or wild animal. Now, this is a double edged sword - if Grandpa begs (in between sips of painful breaths) for euthanasia we can't do it. The only recourse is suicide.
There's too much of a grey area when you allow human euthanasia, that's why its ethically dubious - it becomes a slippery slope much faster due to sentience & consciousness.
As opposed to animals, which aren't thought to possess self awareness/consciousness.
Situations where we consider euthanizing animals humane: When it would be inhumane, as a veterinarian acting as the guardian and protector of animal welfare, to let them live.
Animals can't beg for euthanasia, so out of compassion, we allow them to pass through the phases of irreparable pain and suffering, to hasten the inevitable, skip the pain and pass on to death.
Thats also why convenience euthanasia is frowned upon.
Shed any light? 🙂