To me, a sensitive person is one who picks up on your feelings quickly and with ease, and who has kindly ways of easing your day or showing that they care.

What you are describing in this instance is not, to me, sensitive.

Instead, he strikes me as defensive. Anger is often a defense for some thought or emotion that the person does not want to admit to or experience. His expected anger over what you would say about his driving strikes me as his way of defending himself from actually facing, discussing, and addressing the driving issue that you would raise. It is his way of putting the blame on you and therefore avoiding his own issue.