Why would a guy not admit he likes a girl?

It's possible he's embarrassed about liking the girl. It's another possibility that he has a very low self-esteem so he's not very confident about telling the girl he likes her. Maybe he's just waiting for the right moment to tell her. If you want to confront the issue, take him somewhere private and just ask him if he has anything to tell you, ask if he likes you, or tell him that you've noticed him acting differently around you and you think he likes you. Reassure him that it's ok if he does despite how you feel. Even if you do confront him, he still may lie about it because he's embarrassed or afraid of what you might think.