It is understandable that if he is a supervisor he would be cautions in pursuing subordinates at work. Usually it is best to leave work and pleasure separate. Of course, there are many people that meet at work and get together.
For him though, you may have to see if from his point of view- he is a supervisor and it would be unethical to date an employee. (he could fear being charged w/ sexual harassment, he could understand that people break up and does not want to have to deal with that person after that at work, etc) It is between the two of you how to go along with this and weight in the pros and cons.
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