The answer lies in the question. The fact that there is no lack of problems in the world is exactly the reason why we shouldn’t produce more people who will suffer from some of these problems, and who will even exacerbate some of the problems in the world.
And of course there is no contradiction between not procreating and trying to help mitigate problems in the world. In fact, parents have much less time to deal with the world’s problems, so if these are so important to them that they recommend others to focus on them, it makes sense for them not to reproduce in order to free up as much time as possible for themselves to deal with the multitude of problems in the world. Children take up lots and lots of time, energy and resources, therefore precisely those who make the claim that there is no shortage of problems in the world are the last ones who need to reproduce because in doing so they will increase the problems because of the harm their children will do, because they expose their children to all these problems, and because they dramatically reduce their possibility to take care of all these problems because they will have to invest most of their time in the children they decided to produce instead of all the problems in the world.
What is the logic in the claim that because there are many problems in the world, one should not focus on one of the main factors in increasing existing problems, one of the main factors in creating new problems, one of the main factors in increasing the number of people exposed to problems, and one of the main factors in reducing the ability to deal with the many problems that exist in the world?
Of course, there is no logic in such a claim and its entire function is a diversion to some irrelevant issue instead of debating the argument itself.
The fact that there is no shortage of problems in the world is the last thing that can challenge anti-natalism. And it should be the first thing that challenges everyone who is considering creating more people in this world full of problems.