Stories only happen to people who can tell them.
The idea here is that a life is full of events, but events become stories only when someone notices them, shapes them and passes them on. Two people can live through the same delayed train or awkward family dinner, and only the one who pays attention to the odd detail, the turn of feeling, or the funny line will end up with something worth telling. In that sense, stories don't simply happen to us. They are made by the telling, and the teller is the one who finds them.
This fits the Southern American oral tradition that Gurganus wrote from, where memory is kept alive by people talking on porches and at kitchen tables. It also echoes the view, common in philosophy and psychology, that we understand ourselves through narrative. I can't point to the exact original source of the line, so I'd treat the wording with some care.
Today, someone might try this by spending two minutes each evening writing down one small moment from the day, or by retelling a mishap to a friend. Practiced this way, an ordinary week starts to look like a life with plot and meaning.