When you debunk something you show it to be false. Many magicians, including Houdini and Penn and Teller, have worked to debunk the idea that magic is anything other than a very clever illusion.
To debunk something is to prove it wrong. The idea that music education is frivolous and should be the first item cut from the budget is something that music teachers work hard to debunk — in fact, they've done it by proving that students perform better in schools with strong music programs. The verb debunk was first used by an American writer, William Woodward, in 1923, to mean "take the bunk out of something." Bunk means "nonsense."