This one came across my YouTube feed recently, and it made me angry on behalf of the air traffic controller. There is a certain etiquette when speaking on a frequency between pilots and air traffic controllers, and it's not just for fun. It's for safety!
Every instruction that an air traffic controller gives is a contract between the controller and the pilot, and the confirmation that you agree with the instruction given is to read it back along with your call sign. This lets the controller know that the right pilot understands and will execute the command given. On a busy frequency, an air traffic controller could be talking up to 20 or more airplanes at the same time, so instruction confusion is a very real possibility.
I think this pilot was just having a bad day. However, it's no excuse!
When the pilot checks on, they did it properly by identifying themselves correctly by their call sign, but in the follow-up transmissions they only reply to the controller without their call sign. This causes the controller to have to do extra work to verify the right airplane is responding to their question. And by this point you can tell the pilot is getting angry because someone else in the cockpit responded to the controller, other than the pilot that was talking.
After the second pilot takes over for a bit, there are a few more transmissions from the other pilot. But the first pilot comes back on again and seems to be making a mockery of the situation by spelling out the call sign in a somewhat sarcastic and angry tone. It's completely obvious that this pilot is doing it just to be stubborn, and still he messes up the radio transmission, which causes both the pilot and the controller to get angrier. It finally erupts when he doesn't read back properly again, and the pilot seems to get mad that their shorthand radio transmissions aren't good enough for the controller.
The Controller Was 100% Right
In this case, the controller is absolutely right and the jerk of a pilot was in the wrong. Per federal regulations and air traffic controlling manuals, a pilot must read back and acknowledge any transmission.
2-4-3 PILOT ACKNOWLEDGMENT/READ BACK
Ensure pilots acknowledge all Air Traffic Clearances and ATC Instructions. When a pilot reads back an Air Traffic Clearance or ATC Instruction:
a. Ensure that items read back are correct.
c. Ensure pilots use call signs and/or registration numbers in any read back acknowledging an Air Traffic Clearance or ATC Instruction.
The fact that the pilot wasn't clued in when the controller had to remind them multiple times before to read back call sign and instructions was an even bigger problem.
Safety First, Always
While we don't know how busy the frequency was at the time of the transmissions, it does not negate the fact that if not read back correctly, it puts the liability on both the controller and pilot. A huge part of air traffic control is read back, hear back. It's a safety measure in place to ensure the pilot doesn't mishear the pilots and the controller verifies what they heard.
There is no doubt in my mind that this pilot was being extremely stubborn (the nicest words I can think of) to the controller, after having been reminded multiple times of their responsibility to read back. This pilot absolutely needs to get pulled into the chief pilot's office and be reminded on his responsibility with proper radio procedures.