If people are not willing to take responsibility for children they should not have them. Why should I pay for their mistakes?
Because "their mistake" might in the future be breaking into your house at 3am.
The trouble with the pure libertarian approach is that it forgets how often some people make their problems your problems.
Don't get me wrong. I'm actually registered Libertarian and understand where you're coming from. There is a good moral argument for your position. You're right, you shouldn't have to pay for someone else's mistake.
But one way or another, they will make you pay. Sometimes it is better to get out in front and handle their problem in your way. If you leave it to them, they'll end up screwing you.
Where did I say you should? I simply responded to the statement that people should not have children because of a certain set of criteria that someone else posted.