funny how as usual you give 1/10 the story.. the other 9/10th was that the PLO {remember them} was using Lebanon as a staging area to terrorize Israel, after being asked by Israel to do something about Yasser Arafat and the PLO, Lebanon did nothing, so Israel took matters in their own hands.
They defeated the PLO and sent them packing, Their mistake was in not executing Arafat and the other top leaders of the PLO. Their second mistake was in not leaving Lebanon after they won.