My birth mother took (what I considered) a sick pride in never sharing any of her recipes. She was a good average cook, but nothing spectacular. Just basic meat and potatoes kind of cooking. She would never let any of us children look in her little metal recipe card file. I remember, one day, feeling quite the juvenile delinquent when I found the file while she was gone for the day. I fiercely copied as many recipes as I could in the time I had. Did pretty well, but didn't get as many as I'd wanted, so...they're who knows where now.
I love to share my recipes and always provide the recipe(s) when I gift someone with something homemade.
When our youngest son got married, I handwrote 100 of his favorite recipes from his childhood and gave him and his new bride a personal "mom" cookbook. Did a similar thing for our daughter when she married.
I have recipes that I prepare that belonged to my great-grandmothers and I love them. I can't imagine such treasures being lost just because someone didn't want to share them.