9 times out of 10, what I really feel is that I've got that person completely figured out, or I've lived through a similar experience enough that the story-telling triggers the memory of MY experience.
Even worse is seizing a pause in the conversation to, "tell you about my similar experience" or jumping too quickly to advise, "have you tried...." The first is where I take over the conversation with my own story (NOT listening) then, a "have you tried" which is telling someone what to do (advice disguised as a question)
Taking turns can be a great way to be in conversation; notice who is doing more of the talking? What more can you learn by asking one of my toolbox favorites, "what else?" and "tell me more (about)"