I think this comes out of jealousy , sometime a person want to be like that person or want to be a friend for this person, and he can't admit so he keep provoking him/her and try to fight with him/her.
Sometimes it is because the other person is bad and feel that he is less than than the other one, so he always try to provoke him/her and cause problems to make a show infront of others.
Something like that happened to me in the university ,it was out of jealousy because i was clever and get always full marks, these girls are sisters and always try to make problems with me, Once i stopped them , one of them started to talk to me and tell about her issues.