I'll add this to the above solid points. Maybe we should ask the opposite question: if there is NO God, why is there good in the world? Why should there be? According to atheists, we are just animals. And ultimately, we are just blobs of chemicals with no purpose and no destiny. It's odd to imagine how a concept like love, which is difficult to even define, could emerge in these chemical blobs that are so otherwise focused on meeting their own basic needs and desires. If we are really without purpose and meaning, it is just weird that something WITH purpose and meaning like love could arise.
Also frequently overlooked in this discussion is man's role in this. Man brought, and continues to bring, sin and evil into the world. Man exploits and murders and rapes and steals and abandons and oppresses man. Mankind does evil, and then runs to God and demands He clean up the mess.
The only solution to evil is to either destroy creation or destroy free will (which is essentially the same thing). If man is not free to do evil, man is not free to love, either. Destroying love would be more evil, however, so it makes evil....well, a necessary evil.
This still leaves the issue of "natural" evils like cancer, earthquakes, famines, etc. On the one hand, man's fingerprints are often on these horrible things. For example, consider the famines that emerged in the Soviet Union thanks to the "genius" of central planners.
But to the extent that natural evils are truly natural, it is imperative to remember the imperfections introduced into the perfect world during the original fall of man. Mankind began to die the moment it began to sin. Longevity shortened and continued to shorten after the Flood. There is considerable reason to believe that genetic imperfections were also introduced into the human race, again resulting from man's free will. This gets back to what I mentioned earlier: we cannot overlook the role that man had in creating the world in which we now live.