I can't shake the feeling that you're only arguing about the rights of the parents and completely ignore the rights of the child.
A brainless child cannot make choices, so who should make choices for it? Usually the parents at first, but what if their choices are objectively bad for the child? Does their right to make choices override the well-being of the child? Should parents be allowed to give their children into slavery to pay off their debts for example? Would it be tyranny of the government to override that choice?
And your assumption that staying alive is always the preferable choice is flawed given that plenty of people with terminal illnesses do want to choose to die rather than continue suffering. In their cases there is also a debate about whether or not the government should be allowed to forbid them the suicide option. What do you think about that? Should they be allowed to choose death or be prevented from doing "significant harm" to themselves and slowly wither away on life support?
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