Apologies if I offended, but my objection stands. You invented a non-existent premise, then based an argument on it.
I've heard it many times both on RF and in person (more on internet, though). I just put it all in one sentence.
The first, the idea some people say when they don't believe god exist (with christian backgrounds) is if he did, he would have been much more kind and benevolent as christians say he is. By that phrase (and on this thread too), they are comparing god's character with what he would "supposed" to do if he would have aligned with his character. In that respect, some say god does not exist because if he did, we would not have children dying (and other reasons they list).
Another very very common flip is christians say god exist because they have seen god work in their lives, work in others lives, what they call miracles, healing (like my co-worker on her missionary trip), and so forth.
I don't know if you've encountered these premises but you can find it all over RF and the latter in every christian and church sermon.
Believers would say god exist because he does X in people's lives and their own. Many people who says god does not exist because he neglected to do X (as christians say god should do). While there are many other arguments, they are both two sides on the same coin cause it assumes in both cases god has some influence on people whether he chooses not to heal some children or those that are healed christians say god has played a part in their healing.
How did not parties (those who formed either argument) come to their argument only on whether god is absent in healing the child or have a role in that child's healing?