I used to be that family member that wouldn't go in a "little airplane." My sister got her ratings at a Part 141 school and I refused to go with her. Though I never had problems with flying as a passenger in big jets, I said, "no way, those little planes crash all the time!!!" I even got very upset when my parents went up with her, and my rule was that they were not allowed to both go with her at the same time. She never really pushed me to go with her, but just told me how much fun it was and how much I would love it. Then one day, I decided to take a flying lesson. I don't know why I changed my mind, but I'm so glad it did because that was a life-changing decision for me.
I think that people just don't like feeling like they have no control. Don't take it personally that your family/friends don't want to go flying with you. I am sure they have no doubt that you are a wonderful pilot.