Q: Why do we Suffer?
A: We cannot understand how G-d controls the world. Rabbi Yannai says in Pirkei Avot (4:15) that we do not comprehend why wicked people live peacefully, while righteous people suffer. This issue also appears in Kabbalah.
Adam and Eve were commanded not to eat of the tree of Knowledge of Good and Evil. In Kabbalah it is explained that had they waited for only 3 hours until Shabbat the fruit would have become permissible. One of the interpretations in Kabbalah of the prohibition to eat of the Tree of Knowledge is that one should not attempt to understand why there is good and evil in the world. On Shabbat, with the coming of Mashiach, it is possible to know and understand retroactively why Divine Providence brought good and evil to the world. The Lubavitcher Rebbe writes, in reference to his own personal vision of the future, we will then exclaim: "I thank you G-d for all of the bad you have done for me!"
In the same vein, Chassidut interprets that the fruit of the Tree of Knowledge of Good and Evil represents the attempt to reconcile between Da'at Elyon, (the higher consciousness and perspective on reality), G-d's perspective on reality, which perceives all events that happen in this world as truly good, and Da'at Tachton, (the lower consciousness and perspective on reality), man's perspective on reality which experiences bad, pain and suffering in this world. Before the consciousness of Shabbat, this reconciliation within the consciousness of man cannot be made.
We must believe that all that G-d does is for the good of the individual and the whole. From the Book of Tanya in chapter 26 we learn that good is from Olam D'itgalia, the Revealed World, while bad is from Olam D'itkasia, the Concealed World. The Concealed World, represented by the first two letters of G-d's Essential Name Havayah, yud kei, is from a higher source than the Revealed World, represented by the second two letters, vav kei.
Suffering is a trial. From Igeret Hakodesh (Ch. 11) we learn that all great men have trials. When one successfully negotiates a trial, he merits higher light from the Concealed World, which is much more than he would have merited from the Revealed World. One who successfully negotiates a trial can even merit to turn bad into good.
The world is full of suffering. The Kuzari devotes an entire chapter to the question of why animals suffer, and why we find suffering at every level of life on earth. According to Kabbalah, suffering is part of the rectification of the world. When the world will be rectified, there will be no suffering at any level. As we approach the revelation of Mashiach, suffering peaks, as all the fallen sparks must be redeemed. These are last moment rectifications, similar to the last minute "pressured" preparations immediately preceding Shabbat candle lighting. When people go through difficult situations, rectifications take place.
The Alter Rebbe, Rabbi Shneur Zalman of Liadi, explains that for the sake of redeeming fallen sparks, it is better for one to suffer, even though because of the suffering he is unable to properly serve G-d, as he has no peace of mind. This is even preferable for his soul than if he would be a completely righteous person without suffering.
May we soon merit the true redemption and the end to all suffering.