Does he like you if?

Depends on the situation. Sometimes, I avoid woman's eyes completely in public because as an average looking man, I get the snobbish looks as though my eyes upon them ruins their divinity. At work, I don't do anything or say anything around women unless it is directly focused on the task at hand, so that I don't get fired for harassment. I don't approach women at all anymore, have no idea how negatively they will react. I don't do much with teens, somebody may think I'm being a dirty old pervert who will try to have sex with underage girls. In addition, there is the feminist men-hating mentality that is so open in our society.
As you can see, some men are consciously giving women all the space they could possibly want. Not your fault, 16 years of men bashing has damaged our country far worse than 9/11. That is realism.

Maybe,

He might be shy.
(after all being shy is a great thing, it tells he play no games)

If he liked you he would want to keep your gaze or show something positive. I think guys do that when they think you like them, but don't like you