This is the greatest question, to the extent, within the “ethics of our fathers” it states clearly “we understand not the tranquility of the wicked nor the suffering of the righteous.”
It also states that when Moshiach comes, God will say, “all the suffering (which anyone who has an inkling of Jewish history knows, the holocaust was one of many!!! times a third of our people were mercilessly butchered,) I did it only for you.”
Why do people suffer?- if you look at the physical, vegetative and animal world, it seems to be a very peaceful non-traumatic existence.
You see, a person ultimately has a single pleasure and that is accomplishment.
Now in order to accomplish, well it must be self-directed (for if I force you to give charity, it is only survival, not overcoming your innate selfishness based on compassion.)
In essence a human being is a composite of selfishness, our first and perhaps primary state (as the Alter Rebbe relates, the animal soul is the person’s primary identity) as well as ideals.
However to actualize us into living our ideals… (for most people are content in believing how things should be… And usually it is not suffering, rather comfort which inhibits, for by nature when we are in a hammock we are very loath to start planting, pruning, picking, hence reaping and benefiting.)