Rushmore

Max Fischer (Schwartzman), an eccentric 15-year-old, is a scholarship student at Rushmore Academy, a private school in Houston. He is both Rushmore's most extracurricularly active and least scholarly student. He spends nearly all of his time on elaborate extracurricular activities, not at all bothered how it affects his grades. He also has a feud with the school's headmaster, Dr. Guggenheim.
Herman Blume (Murray) is a disillusioned industrialist who finds his operation of a multimillion-dollar company to be tedious. He is upset that his marriage is failing and the two sons he's putting through Rushmore are impolite and obnoxious brats spoiled by their mother. Herman comes to like Max, and the two become good friends. Max is proud of Herman's success while Herman is interested by Max's arrogant persona.
Rosemary Cross (Williams) is a widowed teacher who arrives at Rushmore as a new first grade instructor. She joined Rushmore after the death of her husband, who was also a former Rushmore student. Max quickly develops an obsession with Rosemary and makes many attempts at pursuing her. While she initially tolerates Max, Rosemary becomes increasingly worried by his obvious infatuation with her. Along the way, Blume attempts to convince Max that Rosemary is not worth the trouble, only to fall for Rosemary himself. The two begin dating without Max's knowledge.
After Max attempts to break ground on an aquarium without the school's approval, he is expelled from Rushmore. He is then forced to enroll in his first public school, Grover Cleveland High. Max's attempts to engage in outside activities at his new school have mixed results. A fellow student, Margaret Yang, tries to befriend Max, but he acts hostile towards her. Rosemary and Blume attempt to support him in his new school.
Eventually, Max's friend Dirk discovers the relationship between Rosemary and Blume and informs Max as payback for a rumor Max started about his mother. Max and Blume go from being friends to mortal enemies, and they engage in back-and-forth acts of revenge. Max informs Blume's wife of her husband's affair, thus ending their marriage. Max then puts bees in Blume's hotel room, then Blume breaks Max's bicycle with his car. Max cuts the brake lines on Blume's car, for which he is arrested.
Max eventually gives up and explains to Blume that revenge no longer matters because even if he (Max) wins, Rosemary still would love Blume. Max becomes depressed and stops attending school. He becomes reclusive and works as an apprentice at his father's barber shop. One day, Dirk stops by the shop to apologize to Max and bring him a Christmas present. Dirk suggests Max see his old headmaster in the hospital, knowing Blume will be there. Max and Blume meet and are courteous, and Max finds out that Rosemary broke up with Blume. Max begins to apply himself in school again, and he also develops a friendship with Margaret, whom he casts in one of his plays.
Max takes his final shot at Rosemary by pretending to be injured in a car accident, soliciting her affection. When she discovers that Max's injuries are fake, he is rebuffed again. Max makes it his new mission to win Rosemary back for Blume. His first attempt is unsuccessful, but then he invites both Herman and Rosemary to the performance of a play he wrote, making sure they will be sitting together. In the end, she and Blume appear to reconcile. Max and Margaret also become a couple.

Question: Who is Max Fischer fueding with?
Answer: Dr. Guggenheim