He wants to step up your relationship
Sounds like he is a guy who doesn't have much confidence. Giving strong eye contact can nerve him out. Make him feel awkward.Why does he avoid eye contact now?
Depending on what's going on, it can be a number of things. He could be lying, he could be thinking about something serious and he just might not be interested. Ask him outright if there's something going on, that's the best way to know for sure.Why does she avoid eye contact?