This is a loaded question, and one that requires more than a single blog post to explain, but I’ll give you a basic explanation.
I’m going to start by saying that sometimes when people ask this question or a variation of it, they don’t always want the answer or explanation. They just want someone to know that they’re upset and hurt, to know that they have a problem with something about the whole concept, so you need to acknowledge their feelings about it and why they feel this way. I’ll say it again: You need to acknowledge their feelings and why they feel this way. If you don’t, you might make them feel worse and put them off even more. For example, when you’re hurt, sad, or angry, you don’t need someone to tell you why you feel this way or why you don’t have to feel this way, you need them to acknowledge that you’re hurt, sad, or angry first. You need to know the other person is listening and actually cares. Even so, you still might not want the explanation afterwards. It’s like stubbing your toe; you don’t want someone to explain to you why your toe hurts and that it’ll feel better in a minute, you just need them to be sympathetic and to get you some ice. Once your pain is acknowledged and it begins to subside, then you’re more open to someone explaining the intricacies of bruising and what to do about it, assuming you even want that explanation.
As for the explanation, evil is in the world because God gave us the ability to make moral choices, and we don’t always make the correct ones. When God created the first humans, He gave them a single rule, a choice, and the ability to think about and make a decision one way or another (Genesis 2:15-3:24, see also the first part of chapter 3 on the choices of their sons). Humans ever since have continued to be able to make choices. In order to have a choice to do something, we must also have the choice not to do it, so God gave us these choices and the ability to make these choices on our own. We can do the right thing that God wants, or we can do the wrong thing that God doesn’t want. The God of the universe, who literally knows everything and what to do about it, lets us tell Him yes or no because He wants us to be able to choose Him. He loves us and gave us the ability to love Him back or not as we so choose.
If God stopped every evil thing from happening, He would essentially be taking away the volition he gave us in the first place, and then we’d probably be upset about that instead of our current predicament. God wants to love us, and He wants us to love Him back, but love isn’t love unless it makes a choice. God isn’t going to force Himself on anyone. God cares very much about our choices and it hurts Him (and us) when we make the wrong ones, yet He wants us to be able to choose. On top of that, even if we make the wrong choices or are the victims of someone else’s wrong choices, God can still turn that around to work in our favor. God is powerful enough to let us all make our own choices while still being in control of everything.
Several related posts:
Love and Volition
Sovereignty of God and Volition of Man
God, Volition, and Natures
God Respecting Your Decision
When God Cannot Give to You
Volition and Personal Responsibility
When Affliction Is Good
Choice and Circumstance
An Allegory on Judgement and Mercy
The Time to Make a Choice