In Berlin at the end of World War II, Wilhelm Furtwängler (Stellan Skarsgård) is conducting Beethoven's 5th Symphony when yet another Allied bomb raid stops the performance. A minister in Hitler's government comes to Furtwängler's dressing room to advise him that he should go abroad, and escape the war. The film then jumps to some time after the Allied victory, and we see U.S. Army General Wallace (R. Lee Ermey) task Major Steve Arnold (Harvey Keitel) with "getting" Furtwängler at his denazification hearing: "Find Wilhelm Furtwängler guilty. He represents everything that was rotten in Germany".
Arnold gets an office with Lt. David Wills (Moritz Bleibtreu), a German-American Jew, and Emmaline Straube (Birgit Minichmayr), daughter of an executed member of the German resistance. Arnold questions several musicians, many of whom know Emmaline's father and say that Furtwängler refused to give Hitler the Nazi salute.
Arnold begins interrogating Furtwängler, asking why he didn't leave Germany in 1933 like so many other musicians? Why he played for Hitler's birthday? Why he played at a Nazi rally? And why his recording of Anton Bruckner's 7th Symphony was used on the radio after Hitler's death? Arnold gets a second violinist to tell him about Furtwängler's womanizing and the conductor's professional jealousy of Herbert von Karajan.
In a sub plot, Arnold is assisted by a young Jewish lieutenant from the Big Red One. The young officer begins to have sympathy for the conductor as well as for the young German girl who works as a clerk in their office. This causes friction between Arnold and his job investigating former suspected Nazis.
In a voice-over, Arnold explains that Furtwängler was exonerated at the later hearings but boasts that his questioning "winged" him. Actual footage of the real Furtwängler shows him shaking hands with Propaganda Minister Joseph Goebbels after a concert. The conductor surreptitiously wipes his hands with a cloth after touching the Nazi.

Question: Why did tension exist between Steve Arnold and the Lieutenant from The Big Red One?
Answer: Because of the sympathy the Lieutenant felt for Furtwangler and the German clerk in their office.
Alternative answer: Because of the Lieutenant's sympathy for the conductor and the young German girl.