Questions: Dating

Hii there! I need your help!

There is a very shy boy in my college that I like. We are both 21 years old. I thought he might like me as he seemed quite nervous when he was talking to me, he didn't ask me a you, he kept enough distance between us and I have seen him look at me several times and sometimes smile a little (I know these are subtle signs but I thought may be signs). I asked him how he was doing personally and he replied that he was not at all interested in being with anyone and that he should get to know the other person well first and he didn't ask me if I have someone. I told him to exchange social media if I want to ask him something about the school and he said we will meet in person, no need, we are not lost. He never greets first either (I think because he is very shy and doesn't talk to many people). I know his parents are very strict. One time his mother called 2 times when we talked to ask him where he is and why he is late. In social events, he is always with them and he seem kinda lost and unhappy. I believe they influenced him based of his shy and not social behaviour.

Is this typical shy guy behavior to reject someone? Should I give up and move on?