The fact of evil and suffering is probably the most used objection given for not believing in God. While for some this may indeed be a real concern it has been my experience in talking to people is that many are using this as an excuse for not believing in God because they don't want to believe in God. Others project evil onto God because then they don't want to deal with their own evil. Whether they realize it or not the reasons they do these things is because they are rebellion against their creator and their hearts are hard.
But there are good answers to the question of evil and suffering if one's heart is open to God. Ultimately the reason, which may seem strange, is because God is love. Here are two excellent short videos that explain if God is good why there is evil and suffering.
Does Evil and Suffering Disprove God's Existence? - Charlie Campbell
The Problem of Evil - William Lane Craig