Many have assumed that it's a reference to the Civil War Confederacy, but that's not the case at all according to the folks at the school at the time.
BCHS was formed 1954 from The Burlington Eagles / Tomcats, The Florence Knights, The New Haven Tigers, and Hebron Cardinals.
The new consolidated school gave the students a vote. The school authorities were pushing “Bisons” or “Buccaneers,” but the student body was having neither of those. A big movie at the time was Rebel Without a Cause, and the students *rebelled* against Bisons and Buccaneers, and voted Rebels.
The Burlington High School mascot changed sometime in the 1940's, from Tomcats to Eagles.
Earlier, the Belleview Bottoms and Hamilton High Schools had merged with Burlington, Petersburg merged with Hebron, Union closed in favor of New Haven, and Verona merged with Walton.