Several reasons. The main one is that Damon isn't a dummy (most of the time). He knows that if Elena's not comfortable admitting that she wanted him to go on this roadtrip with her, forcing her to admit it isn't going to go anywhere good. Secondly, this is a sign that Elena's feelings for him are growing, and he's going to want to nurture that.

Basically, he's goal isn't to shut her up, it's to encourage her to fall in love with him, and letting her keep her pride and comfort zone with regards to their relationship is in his best interests.