Firstly I agree that he has no "right" to know anything. He needs to realise that the one of the points of breaking up with someone is that they don't have any "rights" over you any more.
There are two types of adultery, so to speak, where a divorce petition is concerned.
If, once you are in a new relationship, you feel like you can tell him you are in a new relationship but manage to keep your new man's identity from him, he can divorce you for adultery with an unnamed person. That wouldn't be so bad, and if he has had no one else but you have, then it would be true.
If however he knows the name, then he can name the other party as co-respondent. That tends to feel pretty crap for the co-respondent . . . it tends to be used mainly when your spouse has left you FOR someone (as just about the only thing that can make the deserted partner feel marginally better).
Coming from the other side of the coin for a mo, when my Ex left me I was pretty devastated and I am sure he told people I was an awful wife. As a religious person I was concerned about what my divorced status would mean for my ever being able to get married again.
A lot of religions/ christian denominations cite adultery as the only real grounds for divorce. There is a slightly ambiguous verse in the new testament to that effect - I interpreted it to my advantage . I divorced my ex for adultery for that reason - I waited till he admitted he had a girlfriend and did the no-name type.
The RCs however believe there is no such thing as a divorce. As a devout RC he may be hoping he will get an annulment. This would mean trying to prove the marriage wasn't really a marriage. I can find you more information if you are interested. If he does get an annulment, although you may legally be divorced, in the eyes of the RC church you are still married: if he marries again he is a bigamist and his children will be illegitimate. And yes they will tell him this, I know from bitter experience!