To the Burmese, the word "Myanmar" represents the oppressive and insane dictator who overthrew a democratic society to institute a communism that nobody wanted, keeping Burma in the dark ages for decades. One of the dictatorial general's feats as he rose to power was quashing civil unrest and rival communist movements among the minority tribes of Burma, and "Myanmar" is the name of the majority ethnicity. You can understand that people remain a little sore about the name change.
"Burma" is an English corruption of the Yangonese word for "Myanmar", but to the Burmese democratic movement--and the many minority tribes--the word represents an ethnicity-neutral name for the entire country.