I agree about the "secrets" issue. I've run into that, myself. Some of the stories have been horrendous.
I've had luck with a few tactics, when someone simply won't share his or her immediate family tree and stories:
1. Look for inherited (or just plain old) items that he owns. Ask him to tell you the story of them. They're certain to open a few doors when he mentions names, who owned the object before, what that person was like, and so on.
I've sometimes hidden a voice recorder (turned on & recording) in my purse, so I can keep the whole thing conversational, without obviously taking notes and still not miss anything important. (If you're not sure that he's speaking loudly enough to be recorded, repeat the important things. Names and locations are always more important than dates. As long as you know the region to look in, you can usually find the dates. Vice versa isn't so easy.)
2. Find some old photos -- really old photos -- of your family, and ask him if he can identify them. Ask him if he recognizes anything (people, objects, locations) in the photos. Get stories. (Take a pencil to write names & places & approximate dates on the back of each photo.)
3. Create a family tree with what you do know, and -- especially if it's an attractive tree, like a fan-style tree -- show it to him. Sometimes, seeing what you do know can give the person more confidence, along the lines of (a) you can help him find the distant relatives; (b) there are blanks he'd like filled in, in the tree, so at least some of those people aren't totally forgotten; and (c) you're likely to stumble onto anything he's hiding, anyway. (I wouldn't articulate that last point. The implication will already be obvious, if "secrets" are the issue.)
If you start suspecting that there really are secrets, it's best to open that door and air them. My best resources for the "skeletons in the closet" are former (divorced) members of the family. Especially a bitter ex-spouse (of a cousin, or whatever) may know the stories and be absolutely delighted to share them... exaggerated of course. (Keep that in mind. You won't be hearing the best version of the tales.)
Once you have an idea of what's being hidden, it's usually easier to find a delicate way of hinting that you already know, with just enough information to make that clear. Then, reluctant relatives can be more comfortable talking about things they've been hiding.