It's an oft-quoted statement. And on the surface it appears simple and self-evident.
But I don't think it's that simple. And more importantly, it ignores what human beings are: biological organisms whose main purpose is to reproduce. I know we don't want to hear that but it's true. We may tell ourselves that we're actually here to worship God, become better people, make lots of money, have fun, etc but the sheer (near) universality of procreation says differently. A few people throughout the ages have chosen not to procreate (Catholic priests and nuns being just a few constant examples) but they are the tiniest of exceptions. (I read a statistic once that stated that throughout history, there has been a near constant 10% of women who have not procreated. I don't know how true this is but even if it is completely accurate I wouldn't include all of those women since they many of them probably were infertile and actually wanted kids).
It's just not realistic to expect people to stop procreating for any reason, especially not something as common as poverty.
The other side of the issue is that I don't believe that most of the people who say "Don't have kids if you can't afford them!" actually care about the children involved. If they did, they would take concrete steps to help the child instead of pointing out the parents' failings. I believe the real reason most people bring up this topic because it gives them a (false) feeling of superiority. They like looking down on the choices of those poorer than them and (falsely) feeling like they wouldn't make the same decisions if they were in the same position.
All of the above is why the cycle of childhood poverty will never end. Poor people are going to continue procreating regardless of their financial situation and those relatively well off don't actually care about other people's kids enough to help them and they like feeling superior in comparison to poor kids and their parents.