Unless I am babysitting for my adorable nieces, I recoil when asked for a story. I am not a storyteller. But, like you, I have many stories to share.
I know many people feel this way. They may be humble, shy, deferential, or non-performative. Professionally, you may be a novelist, a screenwriter, performance folklorist, or a singer/songwriter. But in real life, you may not fancy yourself a storyteller, either.