When I was growing up, I was told that you could never become fluent in a second language, and I believed it. I had no reason not to. I didn’t know anybody who had become fluent at a second language, and I could think of plenty of people who had learned English as a second language but who weren’t fluent.
But how would I know if someone had learned English fluently? If they were fluent, I’d assume they were native speakers. I knew people had learned English as a second language because they weren’t fluent. This is selection bias, where the selection of data you see is influenced by the very thing you’re interested in.
A famous example of selection bias is that of British bombers returning from missions over Germany in World War II. Statistician Abraham Wald advised the RAF to add armor precisely where these bombers were not shot, reasoning that he was only able to inspect bombers that survived their missions. More on this story here.
When I was in college, I had a roommate who had learned Spanish fluently as a second language. I thought “That’s not possible!” though of course it is possible. I immediately began to wonder what else that I thought was impossible was merely difficulty.