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I personally would never euthanize a pet/bird in specific unless I knew 100 percent for certain what their ailment or problem was, and was 100 percent certain that there was no treatment I could do whatsoever.
If it's anything except that, I'm too much of an 'amateur pathologist', to so speak, to let it go. A sick animal, as tragic as the situation is, is also a wonderful opportunity to take advantage of today's medical treatments and care.
But that's just me. I like avian medicine, and if any of my birds came down ill (even with something as serious as what you described), I would first try to diagnose and treat it myself or get a vet to do it. But again, that's just me, I love avian medicine.

It's unfortunate that all your finch's offspring have died. That's why it's always good to have planned breedings where you specifically select the parents, backed up with knowledge in the avian field, versus indiscriminate or accidental breeding, which either lead up to problems immediately or /will/ lead to problems later in the road, perhaps generations later. Finches with good genetic backgrounds and care should reach 10 years (or beyond, in some cases).

I've never had to euthanize any of my pets either. Because of the reasons stated above, I don't think I myself could do it- there's always the minute chance of the miraculous turn-around, you know?
If there would be someone to do it for me, such as a veterinarian, then I would be much more open to the idea and probably would euthanize if it really got that bad. But DIY euthanasia is too hands-on for me, personally- to know that I've killed an animal by my own hands, even if it was necessary, would be to hard to deal with. Especially with pets- my finches are my life and joy.

I came close to euthanizing my fish once, but he recovered, so I'm even less inclined to do it in the future. But I researched acceptable methods. Don't forget "euthanazia" means kind/gentle deat. It does not mean "killing" your animal as that could be a number of ways. There are many ways to kill a fish for instance. But the clove oil I bought was the only over the counter/ do-it-yourself method that was veterinary approved as a method of "euthanasia"

Suppose for instance, you chose to break it's neck, and you didn't do it properly, you would cause a lot more pain and stress to the bird. suffocation is kind of a crappy way to go. When cats and dogs are euthanized, they are anesthetized BEFORE being given the lethal dose.

I think some times you want to wait for them to survive, but, if say an animal had been suffering for like a week, with no sign of progress, then I'd say whatever chance they miraculously survive is not worth more suffering.

Um, I do think about it once in a while. thought about it hard on during Christmas with Warrick, he had a tumor, and the pain meds and antibiotics (they wanted to make sure it wasn't an infection.... ) weren't helping. But since he just started to loose weight, I debated to just let him go with Jethro next to him, but he kept opening his tumor so I took him up to the vet and let them put him down...

When he was out in my hands he seemed a bit more lively but he would just pick when he was in the cage.


I have decided with my gerbils I want them to go naturally unless they went into a severe decline in health/hurting themselves (like Warrick did)

One of our budgies has decided he's in the mood and keeps trying to mount his mom.. which we're not wanting babies at all. So he's in with mom finch right now. They get along pretty well. Or rather, she beeps and he looks at her confused. They don't fight at all. Right now another budgie is in there too, since my boyfriend got sick of them yelling for each other, lol.