In reference to the Sermon on the Mount, Jesus spoke to his hearers hoping for great change. See, they had heard about living differently, but in the Sermon on the Mount, Jesus begins to ask for bold changes. He particularly goes after Jewish leadership with harsh language, which would have been a group of highly influential religious elites, like politicians today.
In that day and age, this would have socially caused quite an uproar. The followers of Jesus grew as a social consequence of this Sermon on the Mount, however, not everyone was pleased with him. Religious leaders (with political interests)didn't understand, nor would they fully believe it was God in the flesh come to dwell among them. Thus, the criticized Jesus and continued to fake their way through their religion with their rituals and their customs. They grew mad at Jesus and later wanted to question him. Obviously, if you follow the story all the way through the end of Matthew, you will find the end of Jesus at least here in the flesh on earth.
Christ enumerated and explained what many of the commandments meant in further detail. Religious authorites of the day didn't feel he had the right or the education to do that. Besides, when someone comes in and says that what a teacher teaches isn't fully true, the teacher is going to feel a little slighted. This is what the religious elites experienced.
Check out a bible commentary online for further information.