The community is called “no stupid questions” so I won’t say this is a stupid question, but damn if this isn’t the most ‘murican question I’ve seen.
Your question seems heavily weighted by the idea that a child is only the responsibility of the people who brought it into the world, which is completely wrong even if it is a fundamental assumption of an individualistic capitalist society like America. It’s a backwards notion to say that someone who has a right to live can have that right taken away because it’s too much of a burden to help them live; life is the exact thing that an organized society ought to be focused on protecting, otherwise what good is that society?
People say “it takes a village to raise a child” and while that is seldom followed especially in America, it is absolutely true. Raising a human being is among the hardest jobs imaginable, full stop. The abilities and needs of that child have to be considered every step of the way because it is among the most important jobs imaginable. If that child is ever treated like a burden, then something in that society has failed. It’s not just the parents’ responsibility to raise them, it is everyone’s.
Should a parent be allowed to euthanize a burden? No. 100% no. That parent needs to enlist help, and honestly help structures should be built into that society.
Lastly, the way you phrase your question is really concerning. “Parents should be able to euthanize their children, because it is better to be dead than feel like a burden.” I hope you can see that whatever convinced you that it’s better to be dead than a burden is utterly wrong. You matter, OP, for no reason other than that you exist <3