I think his dislike of her is more about the way she teaches and treats the students on her program. Teaching dance is what he basically does for a living, when he is not on DWTS, and she gives his profession a bad name.
I thought they stopped dancing when the instrumental music stopped, and the singer was a cappella, and started dancing again when the music returned. To me that was why it was not a problem with the judges, and did not affect their score.