The "problem" of evil is a very complex argument to answer, but the good thing about Christianity is that it is the only faith that can adequately answer it. That is, if you take it as a whole. As humans, we instinctively know that something isn't right with our world. Violence isn't good. Disease isn't good. Natural disasters are not good. Death is not good. The world is full of horrible things that are obviously not good. Yet, scripture tells us the world was created "very good", by a perfect and Holy God. So how do we reconcile this?
For the Creationist, the answer is relatively simple. We could go into depth by pointing out that we need a standard of "good" before we can even begin to discuss if things are good or not, but to simplify it, we can just skip all that and agree that yes, the world as we know it is a very bad one. The question of why can be easily answered by the fact that it wasn't always this way. In God's account of origins, we see the creation of an initially "very good" world. The bad things were not present. Rather, these came in later. How?
One of the good things God created was a human couple. To these, He gave one very simple command: Do not eat from the forbidden tree, or you will die. Of course, they disobeyed, and as a result, the Lord cursed the entire creation. So, it's not a case of God creating chaos out of either failure or malice, but as a just result of sin, and also as a method of reversing it. Theoretically, even an Old Earther should know where it goes from here.
But to the aforementioned Old Earthers, and especially Theistic Evolutionists, this account is erroneous. They have to fit all manner of chaos and evil into a gap between the beginning of creation and the fall of man, and so they make a number of excuses, up to and including attempting to justify obviously bad things as being within the scope of "very good". According to the Old Earth narrative, carnivory, cancer, parasites, and of course death, all existed before the fall of man, rather than being the result of it, and so they actually attempt to say that either "very good" does not literally mean "very good", or that our perception of "good" is faulty, and so they will try to say cancer is actually a good thing.
This is a mindset I will never truly be able to understand. To attribute the horrors sin has brought upon this world to the God who once declared it "very good" is so close to blasphemy that I am astonished by how many Christians come to that conclusion. It is high time we abandoned this disgraceful heresy once and for all.