It Looks Like Someone in the Medical Field Just Walked in.
People who work in the medical field but don’t have a degree in medicine usually don’t call themselves “doctors” and don’t like it when people call them that. Ross Geller probably told that joke at some point on Friends. You won’t believe it, but there are people in the real world who act very much like how you describe them. They worked hard and spent a lot of time over a long period of time to get the highest degree they could get at the time.
Because this person thought he was the only “doctor” in the room, everyone else introduced themselves as doctors and started calling each other doctors. This made the whole thing even funnier. It looks like his plan didn’t work, and he’s no longer interested in people calling him “doctor” at this point.