Well I found something on "wikipedia" about this issue, and from two female woman's rights advocates:
Child support - Wikipedia, the free encyclopediaMelanie McCulley, a South Carolina attorney coined the term male abortion in 1998, suggesting that a father should be allowed to disclaim his obligations to an unborn child early in the pregnancy. Proponents hold that concept begins with the premise that when an unmarried woman becomes pregnant, she has the option of abortion, adoption, or parenthood; and argues, in the context of legally recognized gender equality, that in the earliest stages of pregnancy the putative (alleged) father should have the same human rights to relinquish all future parental rights and financial responsibility—leaving the informed mother with the same three options.
'When a female determines she is pregnant, she has the freedom to decide if she has the maturity level to undertake the responsibilities of motherhood, if she is financially able to support a child, if she is at a place in her career to take the time to have a child, or if she has other concerns precluding her from carrying the child to term. After weighing her options, the female may choose abortion. Once she aborts the fetus, the female's interests in and obligations to the child are terminated. In stark contrast, the unwed father has no options. His responsibilities to the child begin at conception and can only be terminated with the female's decision to abort the fetus or with the mother's decision to give the child up for adoption. Thus, he must rely on the decisions of the female to determine his future. The putative father does not have the luxury, after the fact of conception, to decide that he is not ready for fatherhood. Unlike the female, he has no escape route'.
McCulley's male abortion concept aims to equalize the legal status of unwed men and unwed women by giving the unwed man by law the ability to 'abort' his rights in and obligations to the child. If a woman decides to keep the child the father may choose not to by severing all ties legally.
This same concept has been supported by a former president of the feminist organization National Organization for Women, attorney Karen DeCrow, who wrote that "if a woman makes a unilateral decision to bring pregnancy to term, and the biological father does not, and cannot, share in this decision, he should not be liable for 21 years of support...autonomous women making independent decisions about their lives should not expect men to finance their choice."
The legal concept was tried in Dubay v. Wells and was dismissed. This was not surprising, since legislation in the various jurisdictions currently sets forth guidelines for when child support is owed as well as its amount. Accordingly legislation would be required to change the law to implement McCulley's concept.
I guess there are efforts out there to try to change public policy.