I believe the driver was itching for a confrontation (he stopped Kalanick as he was getting out of the car to start the conversation). It was only after being berated for a minute or two and interrupted that Kalanick's composure started to crack. Before then, I don't think anything Kalanick could have said would have mollified this driver. He had an axe and he was going to grind it. Kalanick could have handled it bet…
Where else should he grind it? Kalanick is the CEO. He made a decision which affects this mans livelihood. Kalanick certainly gets paid enough to face up to people like this. And if he wants to stop facing up to it, maybe he can do something about their pay.
Kalanick was off the clock, clearly on his way home and in a social setting. The driver could have really capitalized on the moment. He could have opened a productive and respectful conversation by saying he was a very early driver and had some feedback - good and bad - asking to sit down at a more appropriate time. That had far more likelihood of achieving any progress.
But maybe he didn't want progress. Maybe he just wanted the satisfaction of venting to the CEO.