J.E.
I'm going to go against the grain here...It sounds like its an issue of trust, not necessarily dating that your son has a problem with. My kids were the same way (my ex cheated and I started dating when they were 13 & 15). They just wanted to know what was going on because they felt so betrayed by their dad. They needed to know exactly where I was and who I was with and what I was doing.
It takes time for them to learn to trust again and he may also be afraid that you're going to leave too.
My advice is to be honest about dating because they need to rebuild trust. It doesn't mean you disclose everything, but the basics. You also want them to understand that you did not deserve to be treated that way. Unfortunately when one parent cheats, its really not just on the spouse because it affects everyone.
Best of luck!
ETA: If we all listened to our children's wishes they would eat nothing but candy, never go to bed, not do their homework, never go to school, etc. Just because you're getting divorced doesn't mean you stop being the parent. I'm not saying disregard your children, but never forget you're the adult.