Killing another living thing doesn't qualify as "euthanasia" if you do it for your benefit, not that being's.

By infant abandonment by giving it to an orphanage (it's not legal everywhere, but in a lot of countries it's perfectly legal and acceptable) you lose both your responsibility and your control over the baby, so you no longer have any right to do so.

And speaking of euthanasia, we really should seriously reban it. We pretty much know how to deal with even the most severe pain - very large doses of opiates to get rid of it, and large doses of stimulants like amphetamines to counter the side effects. War on Drugs is the reason why we don't routinely do this to people in severe pain.

We don't have a magical cure for depression, but if someone is depressed, they cannot make rational decisions for themselves anyway, so they cannot decide to kill themselves legitimately.

Once you cover these casese, there are zero legitimate arguments left for euthanasia.