well, the first reason is that back then, in Dante's time, "comedy" didn't really mean funny. In this case, it meant that even though the whole story/poem is full of despair and torture and torment, it actually ends with a happy ending. Back in Dante's era, this meant that instead of being a tragedy, this epic poem was considered a comedy.
Consider Shakespeare's work Romeo and Juliet. It ends with the two young lovers dying, right? That is a tragedy. There is no happiness there. But at the end of Inferno, Dante the Pilgrim actually succeeds in his goals.
