I will only guess at the reason that I'm familiar with - I'm sure there are many. Getting recipes from my mom and aunt was like pulling teeth. It wasn't even, "No! It's a secret!". It was, "Sure honey, we'll make it tomorrow and I'll show you how." This happened with my mom all the time trying to find out EXACTLY how she made the German pancakes I loved. There was no recipe or even real measuring - it was all in her head. Pretty much every time I was visiting and interested in having her show me how to make them, it was, "We'll do it first thing in the morning". The next morning I'd wake up to the smell of freshly made pancakes.

My guess is that much of it was a need to feel wanted and useful. Even when I wasn't trying to get a recipe out of her, she would always have her feelings hurt if I wasn't hungry or something and she couldn't make me breakfast, lunch, or dinner. Cooking was something she was really good at, and I guess she just wanted to feel useful and needed.
She got a bit better about it in the last few years of her life (though I still was never able to get the pancakes down!), and my dad is pretty good about it, but the way he explains things (also no measuring) is so aggravating that I've actually just shot video with my phone so I can try and duplicate the process.
