Is there any positive purpose to our suffering in exile?
Exile is a descent for the sake of an ultimate ascent and demonstrates the superiority of light over darkness.
The teachings of Chassidism explain the great spiritual gains of our descent into exile. It is a descent for the sake of an ultimate ascent; it demonstrates the superiority of light that proceeds from darkness, and so on. Thus it is written, "I will thank You, G-d, for You have been angry with me." When Moshiach comes, Israel will thank G-d for the exile, for then they will appreciate the great gains it brought about. The previous Rebbe of Chabad once said, that when Moshiach comes, people will hanker after the days of exile. They will regret the lost opportunities to devote themselves to Divine service and overcome challenges.
At the same time, though, this knowledge does not dampen our desire and will to leave exile. We still cry out, and truthfully so, "for we hope for Your salvation all day long." In other words, a Jew harbors two opposite feelings simultaneously. On the one hand, he believes that exile has a positive purpose (although we won't completely understand or appreciate it until after Moshiach comes.) On the other hand, he cries out from the bottom of his heart to leave the exile.
The truth is that all the explanations on the positive aspects of exile are only addressed to the mind. As far as the feelings of the heart are concerned, however, the bitterness of exile makes all of these explanations unacceptable. That is why, even after all the explanations have been offered, Jews still ask and cry out in prayer that the exile be annulled and the Redemption should come immediately.