Telling stories is a powerful human need, closely aligned with the need to create. That lesson is continually reinforced for me, moving into high relief each time I get involved with a new writing group. What is your preferred method for telling a story?
Although people can sometimes struggle when beginning their story, if you stay focused and ask pure questions - i.e. ones for which you don't have an answer - that story often slowly emerges. What have you observed about people who struggle as their story unfolds? In my experience, the quieter I remain after someone gets started, the deeper the storyteller goes.
Sports and work related stories can act as neutral territory for those not temperamentally inclined to share personal stories. I've met few people who don't enjoy sharing stories from these domains. And even most neutral topics reveal a great deal about the storyteller. Because telling stories - topic aside - is about tapping into what is inside of us, feeling heard, creating. How many people have you met who don't want those things?