Its funny how compasion seems be be indicated by size and intellect - i mean you wouldn't brick your dog or cut its head off, but because a fish seems to show no emotion it feels ok.
What about isolating it and letting it die natrually - i wonder how many actually make a fuil recovery (unless there are physically irrepairable)
I see what you mean, but we do take cats and dogs to be euthanised; if vets could euthanise things like neon tetras, then that would be great, but it's not very practical or economical!
Isolating things is a good idea, and many fish do recover, but there are some cases where you know the fish isn't going to pull through, or it's clearly suffering, or even, to go back to shoaling fish like neons, the stress of being separated from the shoal to prevent diseases spreading, make home euthanisia the best option.
Personally I find knowing that I can painlessly destroy a fish, if the worst comes to the worst, a great relief; in the past I've had to watch fish clearly suffering, and it's an awful, distressing thing, both for the owner and the fish.
I think every fishkeeper should keep a bottle of clove oil handy for those times.
'Bricking' or decapitation are probably good alternatives, if you have the stomach for it and can do it properly; I know I'd be too shaky from weeping to be able to