Frankly I don't think women have a right toward abortion or that men have the right to opt out of child support. But the argument made for abortion rights is that it is the woman's body that is forced to undergo the stress of childbirth and without some intervention, the child by default ends up the woman's problem and the man can run away.
I have exactly ZERO sympathy for men who like to cry about child support. There are cases where I think the courts are unfair or demand ridiculous amounts, but in principle... the man needs to be held accountable.
From a macro-level concern, the other issue is that if a man is not held accountable, he can go off and impregnate many, many women and shirk the responsibility. The woman, even if she goes for abortion, has to take some action and go through some crap. The man, without child support laws, can run rampant and pay NO PRICE... a total free-rider.
The only problem I see is when these no-responsibility over-procreators get so many child support cases that the state can do no more to them- they might as well go impregnate some more. I think they should be sterilized automatically after two such attempts... but that would be doing them a favor on the taxpayers... so they should have to pay for that service themselves or face jailtime.
I also would really like to know why it is that every guy I know who whines about child support can seem to afford all kinds of home entertainment equipment and stuff for himself. Boggles the mind.

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"Man lives in the sunlit world of that which he believes to be reality. But unseen by most is an underworld, a place that is just as real... but not as brightly lit... A DARK SIDE!"
-opening from Tales From the Darkside