I was very upset with my boyfriend. He came to me to ask forgiveness, but I could tell that he was doing this only because I was upset. His overture of seeking forgiveness did not seem genuine to me at all. Under this kind of circumstance, should I have confronted him about his insincerity or should I have just accepted his superficial request and let it go?
It seems in this circumstance that you would be better off talking with him about your impression of his insincerity. This does not mean that you do so right then, when you were very upset. His lack of sincerity could be another event in which you need to forgive him. Your first working on forgiveness may make your conversation about his insincerity more civil and more productive. If you confronted him when you were very upset, without your first starting the forgiveness process, then this possibly could deepen the original argument.
For additional information, see: 5 Ways to Apologize to Someone You Love