There's a lot of rubbish spoken about the idea that God is infinitely good being incompatible with the truth that there's suffering in the world. There are a lot of good anaswers to it from a Christian point of view; the best ones centre on Jesus.
That's not what I'm trying to do here. I'm going to try to show why it's plausible that the idea of an inifinitely good God should lead to an expectation that there will be suffering in the world. I'm not saying these arguments are watertight - it's just to get people thinking. Oh, and they're mostly working from the writings of John Piper.
A) An infinitely good God would want others to appreciate his goodness, power, etc. to the greatest possible extent If God is infinitely good, then he will want people to have an accurate view of things, including his own nature, so that they can enjoy him.
B)God's goodness is most visible when you can also see the absence of goodness You can only see how good things are by comparing them. I used to think the school I went to was ok. It was only when I went into other schools that I appreciated how good it was.
A) and B) imply that a good God should permit the existence of things that are not good.
C) God's power and sovereignty are more visible in him working through and despite evil rather than just working in good. Makes sense. How awesome a god would be who could use even people and actions opposed to him for his purposes!
A) and C) imply that people appreciate God better when seeing him working though evil, and hence that an inifinitely good God should be seen to work even though evil events.