The fact that can be said about any argument does not make it false. But, it cannot be said about any argument.
The argument has to have a specific structure, more specifically, «There is no reason why X could happen because Y. Then X is impossible», where Y is not strong enough. This is a hell of a claim. («There is no reason why God could allow evil because God is good and all-powerful. Hence, God does not exist»).
(Other example of this kind of argument is «There is no reason why extraterrestrials are good and powerful enough because they allow us to suffer in this planet instead of giving us superior technology to live better lives. Hence, extraterrestrials are not good enough or not powerful enough or they don’t exist»)
If Y is strong enough, you don’t care about unknown objections. For example, if God could do everything, including the contradictory things (a squared circle, a free will agent that can only do good), the argument would be completely tight. It would be as tight as «There is no reason why a bachelor married exists because a bachelor is the man who is not married. Then a married bachelor is impossible».
The fact that God cannot do contradictory things opens a leak in this argument. And the leak is impossible to solve. In general, if Y is not strong enough, these kinds of arguments are really difficult or impossible to prove.
See for example, a dog thinking when it is vaccinated: «There is no reason why my master is good because he makes me suffer and a good master would not make me suffer. Then, my master is not good or does not exist».
Imagine the extra-terrestrials doing things that are not understandable by us. This does not mean that they don’t have any reason. Maybe the extraterrestrials does not give us technology because the drawbacks would be much bigger than the advantages and they know why. This does not mean that extraterrestrials are not good enough or powerful enough or they don’t exist.
In the case of God, you should prove that a specific instance of evil E (not all instances of evil are needed for the argument, only one instance will do) is not necessary to produce a great good G. That is, that producing G with not producing E is contradictory. This is completely impossible to prove because:
1. You cannot prove that you know all possible Gs. G could be any greater good that a human could not understand but God could. (See the dog being vaccinated).
2. You cannot prove that you know all the contradictions that exist. If the supernatural realm exists, there may be contradictions that we can’t imagine. For example, the contradictions that see the good extraterrestrials of the example (for example, «if we give them technology, they will self-destruct themselves»).
This is why the logical problem of evil is bankrupt. In addition, even if the argument from evil worked (which doesn’t), only would prove that God is not good or God is not all-powerful. It would not be proof for atheism. An alternative like Open Theism would be as possible as atheism.
It is mostly an emotional argument. The emotion is its entire strength. «How can God allow that children are raped? The horror! The horror!». But emotion is not a logical argument.
But there is no inconsistency Jeffrey. Nobody said that the failure of problem of evil is a reason to believe in God, although if the problem of evil succeeded (which doesn’t), it would be a reason to not believe in God. The failure of problem of evil simply proves that this argument is inconclusive for the existence of God.