To warn someone they may be considered guilty of "insubordination" because they refuse to discuss a personal matter as described when commanded to do so by their supervisor is ...well, I just don't think it's helpful. Sure, it's an "at will" work world, and I suppose it's probably insubordination in someone's world. But in my experience, that's a dog that usually does not hunt well at all in unemployment insurance appeals and it would not be a very good idea for employers who are trying to keep people from receiving unemployment to use it a lot, though it gets thrown around a bit, certainly But in this situation the employee shouldn't be worrying at all about whether they can tell a rude or overbearing supervisor "No I do not choose to discuss this personal matter," without committing some big violation or disobedience.
This isn't the military, this supervisor does not have the power of life and death over you, and this isn't quite an occasion of failure to comply with a direct work related instruction from the employer. Sure, they can fire you for being insubordinate if you refuse to tell them what the other employees really said about their new haircut, or they can order you to kiss their ankle each morning when you walk in the door. But it's not something the employee needs to worry about unduly while dealing with bullying behavior such as this in the workplace.

