The problem of evil has been along standing problem for theism to surmount. Now it may not be a problem for every type of god but it is fatal to a particular kind. Namely a god that is able and willing to end suffering. But as Epicurus said, "Then whence cometh evil?" Over a few thousand years has past and theist have offered answers in-order to try to satisfy that question. Here I plain to go over a few of them and show just how insufficient they really are.
The problem of evil can be formulated as follows:
P1. God is all-powerful
P2. God is good (or omnibenevolent)
P3. There exist unnecessary evil or gratuitous suffering
P4. P1 and P2 conflict with P3
C1. Therefore a god with properties from P1 and P2 does not exist.
The contradiction that exist isn't obvious at first if we don't qualify what we mean by good. I would think that most people would agree that good would "reduce or confront evil whenever possible." If accepting that, then a god that could reduce evil would be considered morally superior to a god who does not. The Abrahamic God is considered the most morally perfect god possible, at least according to the argument of Ontology. So this a pretty thorny issue to say such a god exists and there is evil at the same time.
The theodicies that defend agaisnt the problem of evil break down into two broad categories. There is the natural theodicies and the moral theodicies.
The natural theodicies can be further broken down to four answers.
A. Evil is a necessary counter part to good.
B. Evil is necessary for a short-term or long-term good.
C. Evil is the punishment for sin
D. Evil is only a by-product of natural law
Evil as necessary component to understand what is good is quite frankly absurd. Do people need to go through debilitating diseases to understand what it is to be healthy? Do people really have to starve to death so that others should understand what it means to be well fed? And what do animals gain by going through similar experiences? They are capable of suffering too, you know. Worst of all, such a proposition would make evil eternally necessary. So long as there is good, there would be evil. Clearly not compatible with theologies that would eventually put an end to evil for-once-and-for-all.
Evil as necessary for short/long-term gain is normally what we call as "necessary evil." Open heart surgery is painful, but is is more preferable from dieing from a heart attack. Something like that is understandable to go through but how does that explain those who are maimed or tortured through no fault of there own? How does that justify those who lose his/her life when a sudden earthquake or land slide happens? Gratuitous suffering still seems to be an open question even when granting this answer.
Evil as a punishment for sins creates one of the most reprehensible and question begging mind sets out of any of the others that I could talk about here. Unfortunately it is also one of the most common. When in March 2011 earthquake/tsunami hit Japan, many people believed that God was visiting wrath upon Japan. The same was said of the 2004 tsunami, hurricane Katrina, 9/11, and yes, even the holocaust. This type of thinking categorically denies that it even possible that innocent people would die or suffer in these events... because everyone is evil... Even if we were to grant such an absurd proposition, there still such a thing as overly cruel punishment to the wicked. Which is codified in the 8th Amendment of the U.S. Constitution. So it not like anyone doesn't understand the concept.
Evil as a by-product of natural law seems to make little sense with a all-powerful god. Why does god have to make a universe with natural law? Why not one with magic capable of mitigating evil in the world? Or simply design a better world? God could have just as easily put all life on a Dyson sphere or ring, rather than just on a planet that is prone to earthquakes and bad weather. This really implicates god as having a lack of imagination. Further, even if we were to grant our current state of affairs with natural law as desirable, there still exists suffering that would be unnecessary. If we could know the cure to HIV, cancer, ect., gain knowledge to farming techniques that could end hunger, could accurately predict and prepare for natural disasters... Why wouldn't a good god share such knowledge if he had it?
The moral theodicies broken down into only two answers:
A. Evil is necessary for virute
B. Evil is a necessary by-product of free will
Evil as an necessity for virtue harkens back to "necessary evil" again but this time for the moral equivalent. Yes, it takes danger for there to be courage, suffering for there to be compassion, and anger for there to be restraint. However, nobody ever considers it a moral obligation to rob a bank so that the cop can do his job in protecting or cause a famine so that others can be charitable. I think everyone can see that causing (or allowing) harm to people so that others can work on their virtue is morally shaky at best and engages in "the ends justify the means" at worst. Sorry, but living in a world without cops and doctors (because they are unnecessary) is still more preferable than living in a world that does have them. Finally, what is courage when someone has gained eternal paradise? Whether someone had courage or not at that point would become meaningless.
The "free will" defense in my opinion is on of the most problematic of all. One, it assumes that "free will" is more desirable than having an evil free world. Two, many Jews, Muslims, and Christians believe in predestination. So this theodicy is an apologetic for a very particular branch of Christian theology. Three, it makes an sinless eternal paradise impossible. Four, it may actually be possible to create a world where nobody choices evil. To deny such possibility would force the theist to admit that god doesn't have "free will" or that god doesn't always choose good. If both are possible in god, then why can't he create others that are like him that respect? Again, something like this demonstrates a lack of imagination.
Even after all of this, there still may be theist who would say that "God may still have a morally justifiable reason to allow evil." One, that technically a contradiction because evil by definition is unjustifiable. Two, it is an admittance of lack of imagination on their part, which means this is a statement of faith more than anything else. I am sorry, but I don't have enough faith to override my reasoning and the evidences I see about he world around me.