The Problem of Evil
How can we have an omnibenevolent (all-good), omniscient (all-knowing), and omnipotent (all-powerful) God and still have evil in the world? He is good, so he doesn't like evil, he knows that it is occurring, AND he has the power to stop it. What gives? Augustine wrote:
"Since God is the highest good, He would not allow any evil to exist in His works unless His omnipotence and goodness were such as to bring good even out of evil."

This is the common response I have heard to the problem of evil, and I believe it to be a good one. It still, however, does give me some pause, and I am not alone in this. (In fact, I believe Bishop Barron, one of the largest voices in Catholic media today, has himself admitted that if there is one aspect of the faith that gives him pause, it is the problem of evil.)
So what's my hang up? Well, there have been some truly awful atrocities in the history of the world, ones that I have a hard time grappling with when it comes to thinking about the goodness of God. For recent historical examples, we can look to the Holocaust and the dropping of the atomic bombs in Japan. For current social issues, we can look to child trafficking, the immense suffering of immigrants across the world as they try to find better lives elsewhere, and the physical/mental ailments that aggressively attempt to erode our senses of self.
It is hard to understand how God can be so good, so knowing, and so powerful and yet not put a stop to these things. But upon some further reflection, I may have an answer.
First of all, God gave us free will. He doesn't want to mess with it. It is a GREAT good.
But secondly (and more importantly), God is the greatest good of all. In fact, he IS Goodness itself. He is Love. He is Beauty. He is Truth. If the aforementioned atrocities, as awful as they are, can bring us closer to him and his Sacred Heart, then perhaps it is worth all the pain.
I realize, that, to some extent, this sounds like an insensitive answer. When considering this issue, it is important to realize that we are seeing the grand scope of things with finite minds, and not through God's infinite gaze. In many ways, the question boils down to this:
Do I trust God?