...that he is simply enjoying her company? It has brought him to the brink of flirtation!

And in the latter case he seems amused by her determination to contradict him. He's actually prepared to insist, when she's convinced they never like the same books.
"Books -- Oh! no. I am sure we never read the same, or not with the same feelings."

"I am sorry you think so; but if that be the case, there can at least be no want of subject. We may compare our different opinions."
I feel Darcy might be sort of mischievous here. And imprudently interested in finding out more about her character perhaps?