Gate agents are busy enough without having to explain all the vagaries of deadheading crews. I admire the gate agent's patience explaining it all but I would have told the guy in simple terms -
"These employees are deadheading crew. If you need more explanation or definition of this, here is United's 800 phone number - ask for a supervisor to explain it if you are so upset".

To talk and talk and explain and define to some selfish jerk is a gigantic waste of time. I would have left him hanging. I don't know why some people feel so entitled to know everything that they have no business knowing about (United's policies and protocol for deadheading crews). He needed to sit down and shut up and wait.