By always having a story to match what they are talking about, I appear to be bragging. This is not my intent. But it doesn't matter. They don't hear, "Wow, I'm so excited to meet you- we have SO much in common!" What they "hear" is that Paris thinks she is better than me. Sometimes they "hear" Paris is so rude that she has no respect for me and my accomplishments!
I learned this about 10 or so years ago when I had run into an old college friend who had just started working in my office. We were talking with a group of our coworkers when he started telling a story about his dad almost getting blown up by a terrorist bomb. I was so shocked because we'd been friends in college and I didn't know he shared my experience! Few people had. I asked if he'd been in XYZ country at the time, and began to tell him about what happened to my dad. He looked at me. Looked at my coworkers. And said, very calmly, "I was trying to tell a story. Are you done stealing my limelight?"
You see, he didn't hear "Wow, this girl is really excited to find someone else in the world who knows what it's like to live where terrorist bombs can blow you up." Instead, what he heard is, "Here I am, trying to make friends in my new workcenter and this girl is trying to show me up and make me look bad."
And I didn't realize that to everyone else, I was appearing to cut him down, prevent him from joining the group. That's not what I was trying to do (this was my old college buddy who I was quite fond of!), but that's how it looked to him and the group.
Whether we are NT or Aspie, others don't always think the same way we do. So our job is to figure out how they think and then behave so their mind translates our words and behaviors into the message we really want to give.
And for most people that means trying not to give the impression that we think we're perfect or better than them.