If you were to argue that Dr. Rumack is the most iconic character in Airplane!, we'd probably say something like "surely you can't be serious."
Then you'd respond by saying "I am serious, and don't call me Shirley."
And that would be the end of the argument.
The dour, grim-faced Dr. Rumack surely gets some votes for the most memorable character in the movie, as a key player in many of Airplane!'s greatest moments. As a doctor, you can tell him anything, and in pressure situations, he's the man to trust. He's truly an individual who can keep cool when everyone else is losing it.
Ultimately, Dr. Rumack emerges as a spirit guide of sorts for Ted, providing encouragement in key moments and helping our young protagonist overcome his fear and blossom into the hero he was always meant to be.
Though the dialogue itself is pretty amusing, we can credit the success of Dr. Rumack mostly to master of deadpan Leslie Nielsen. His delivery is tirelessly despite the sheer absurdity of the situations Airplane! presents. He remains gravely serious, never letting on for a second that he's in on the joke.
Just don't call him Shirley.