It does sound quite reasonable when you put it that way. On the other hand, you could also describe it as, "we should starve poor families to death if the mother is sexually active and doesn't use approved birth control." Which sounds decidedly less reasonable to me.

But ultimately my counterargument would be that we should focus on helping people who need it, rather than on not helping people who we think don't deserve it. This country has a puritanical mindset about public help, where we're outraged at any person who receives it who we see as being in any way unworthy. For a pervasive recent example, look at drug testing for welfare recipients. It's more expensive than not doing it, but people love it because we see drug addicts as being evil and therefore unworthy of help.

We need to teach compassion, or at the very least rationality, rather than a punishment mentality.