And just because they have a good relationship means he can't keep a secret from his son? Having a good relationship with someone, even family, doesn't mean that you don't keep some things from them, especially if you have or believe you have a good reason not to tell them.
There are a few fairly plausible reasons why Neil wouldn't tell him he was related to the Burgmeisters, and it's interesting that whenever he tells the MC about his Mom and about how they got together, he seems to have trouble remembering all the details properly which makes it dificult for the MC to ask him about it because he never quite gets the full story. Almost like Neil is deliberately acting forgetful to try and make the MC not ask if he knows he won't get anywhere by doing so.