The argument never addresses the possibility God intentionally created a world that suits him. It leaves this option completely open. It just so happens this is the result Christians claim. Furthermore, the omission is meant to be obvious. Clearly we live in a flawed and broken world, and how could a perfect and powerful God allow that? This actually attacks the Christian worldview as so absurd as to not even be worth mentioning or considering.
A more modern way to view this restates it like this, to state the issue explicitly:
If God is good, he is not God. And if he is God, he is not good.
The existence of cancer in children is also often brought up as a common case-in-point. A child has not sinned. How could a perfect God allow such a thing to happen to a sinless person? He must be either powerless to stop it or a participant in making it happen. Ultimately, this is the problem of how we deal with suffering.
My answer has to come in two parts: one to address the specific and one to address the abstract.
I'll start with the specific. While I can go several directions making abstract arguments for the general problem, that's not helpful in the moment. For the person dealing with suffering right now, I don't want do anything other than be present with them and offer comfort. It's important to make that plain first. When suffering happens, all the other lofty logic we might produce is counter-productive and calloused.
Having stated this, the context we have right now is more of an abstract question, inviting us to respond on that axis at length. Still, I prefer brevity and I'll reframe the problem one final time in order to keep this short. We can reduce it down to this:
Why didn't God create a perfect world?
It is fundamentally the same issue as first posed, and we can answer like this: "He did. Twice." The world as it was first created was perfect. It was only after mankind brought sin into the world that we had any death or suffering. A child has cancer not because of their sin, but because they were born into a corrupted and sinful world. One could argue this itself is a flaw, but the Christian can respond even this was also part of God's plan from the beginning, that the world will be redeemed and anyone who wishes can be with God in Heaven, where there will be no sin, no suffering, and the joy there is so far greater than any previous suffering as to render it meaningless.