At a ball, gentlemen are expected not to be wall flowers; if there is a lady without a partner, it is usually a considerate gesture for the gentleman to offer to dance with her. At social functions, it is usually expected that a husband and wife would like to talk to other people, which is why husbands and wives are generally never seated next to each other at a formal dinner (which often precedes the ball). If a couple wants to spend time with each other, they should do it at home, and not a social function. At a dance, each man should try to the best of his ability to dance with the lady seated to his left and right during the dinner, if there was one, and he must dance with his escort and the hostess.
David, please advise your friend not to be offended; it was probably a well-intended and polite gesture on the part of the dance instructor to offer to dance, especially after he noticed that her partner did not.