Ohio's proposed bill giving veto power to the father of a pregnancy for which a woman is seeking abortion is a terrible idea, simply put. What's more, it's a complete misreading of what the right to abortion is.
Women have veto power in the area of whether or not to continue a pregnancy because the right to abortion is a right to control one's own body. Treating it like a right to the property or custody of the developing child is misguided; the mother has no more claim to the fetus than the father does. The mother does, however, have it implanted in her womb. That's the connection over which the mother has control, and were there a way to transfer the fetus from mother to father - or mother to incubator - more power to the parent seeking custody.