Should a man be allowed to sign away his parental rights to a child if he doesn't want it?

Obviously I don't mean at the kids 10th birthday party, but at birth or before. Like relinquishing his claim to the child entirely. No child support, no custody - it would be like you never had a kid. Personally, I think yes. I agree with pro-choice arguments for women but I think it should be equal. If a woman wants to keep a child and the man doesn't, he shouldn't have to carry a responsibility to it for the 18 years.
Yes, he should be allowed to opt out and sign his rights away.
Vote A
Yes, he can sign away his rights but he should still have some responsibility (financial, etc)
Vote B
Eh, it should be case to case basis.
Vote C
No, he should not be allowed to sign his rights away and should have a responsibility to the child.
Vote D
No, he should not be allowed to sign his rights away but should be able to opt out of the responsibility to the child.
Vote E
No opinion/Poll results
Vote F
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Should a man be allowed to sign away his parental rights to a child if he doesn't want it?
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