The Differences of the Imams

If the Imams of the four schools (madhahib) established all of their rulings from the Qur’an and the Sunna, why have they differed on so many points? How can two authentic narrations from the Messenger of Allah (Allah bless him an give hime peace) appear to contradict one another? When is it acceptable for Muslims to differ over religious matters? What did the Messenger (Allah bless him an give hime peace) mean when he said, “The differences of my Umma are a source of mercy?”