I'll sketch out the basics here as to why 'the problem of evil' is one of the worst objections to believing in God. (Aside from it having been covered to death by loads of philosophers all through the ages, starting with debate in the Book of Job).
The classic Problem of Evil goes a little like this:
P1) If an all-loving, all powerful being exists, it would destroy evil.
P2) Evil exists.
C) Therefore an all-loving, all powerful being doesn't exist.
Problem with it is that it doesn't exhaust all the options. The missing option is that the being could have a good reason to allow evil, probably because it leads to some greater good. Christianity teaches several possible reasons, so the problem of evil falls flat because it's not a sound argument. P1 isn't remotely demonstrably true.
If it's not enough that the rebuttal destroys the Problem of Evil, we actually find that the Moral Argument for God means that the Problem of Evil as an atheistic argument doesn't get off the ground because it is actually evidence for God.
P1) If objective moral values exist, then God exists.
P2) Objective moral values exist.
C) Therefore God exists.
If an atheist uses the argument from evil, they basically admit P2 is true. So that only leaves P1.
Objective moral values are moral truths that hold whether or not anyone agrees with them. So like if the Nazis won WW2 and brainwashed everyone into believing Jews needed to be destroyed, it would still be wrong to gas them.
The only way for there to be objective values is if there is something to compare them to. You can't say something is better than something else unless you have some sort of measure to go by. The only possible objective measure would be a morally perfect entity of some sort. Christianity has that in God.
This doesn't for a second mean that atheists can't make up their own rules and decide love is good, murder is bad, and base it on survival or something. The difference is that anything atheists come up with is purely subjective. So there is no real 'good' or 'evil', just stuff they do and don't like.
So basically, when someone says they don't believe in God because of evil, they either have to admit they're wrong and God exists, or to maintain atheism they have to become nihilists who lie to themselves that anything has any meaning. If they complain about not liking murder, their opinion has no more weight than if they said that they don't like waffles. No one has a right to ban waffles. I'm looking at you Jamie Oliver... you turkey twizzler stealing scoundrel.
Even more simply: believe in God, you can believe that things really are right or wrong; don't believe in God, you can't say anything is truly right or wrong, but you can have your own personal opinion about it.
In short: Problem of evil? No problem...
