The only *slightly* arrogant doctors I have ever met were surgeons. One memory that sticks out was when I was shadowing an ortho surgeon, and he introduced me to his residents. Our 10 second conversation went like this:
Resident 1: "So JFK90787 you wanna be an ortho surgeon?"
Me: "I don't know what I want to be, I am just trying to shadow different things right now"
Resident 1: "Well if you wanna get into ortho, you gotta be the best of the best" (I later looked him up online and found that he graduated from George Washington)
Resident 2: "We do work, that's why we get paid bro"
*choreographed high-fives between resident 1 and 2*
Me:
edit: But I am sure they are both very good doctors and they had much better demeanor for their patients. This was just behind-the-scenes stuff