He's ignoring them because he's being polite. Neither of these answers applies in the U.S. In the states, this girl is either flirting, or giving him a backhanded compliment.

The best post I've seen so far referenced a male student calling a female instructor "sweetheart." It really is a great example of what's going on here.

Either she's flirting with you in an off-the-charts inappropriate way, or she's deliberately being disrespectful. You were there, and whichever of these options is correct should be obvious. Not sure how anyone could confuse the two.