"Is God willing to prevent evil, but not able? Then he is not omnipotent. Is he able, but not willing? Then he is malevolent. Is he both able, and willing? Then whence cometh evil? Is he neither able, nor willing? Then why call him God?"
-Epicurus (341 - 270 BCE)
Or, to put it in problem form:
If an all-powerful and perfectly good god exists, then evil does not.
There is evil in the world.
Therefore, an all-powerful and perfectly good god does not exist.
Or you could refine it, as has been done:
God exists.
God is omnipotent, omniscient, and perfectly good.
A perfectly good being would want to prevent all evils.
An omniscient being knows every way in which evils can come into existence.
An omnipotent being, who knows every way in which an evil can come into existence, has the power to prevent that evil from coming into existence.
A being who knows every way in which an evil can come into existence, who is able to prevent that evil from coming into existence, and who wants to do so, would prevent the existence of that evil.
If there exists an omnipotent, omniscient, and perfectly good being, then no evil exists.
Evil exists, therefore...