What do you do if you think your crush likes you and shows it but won't go out with you?
The best you can do is to let him know how you feel. He might be afraid of asking you out because he thinks you will reject him. Show him that the feeling is mutual and he will ask you out with much ease.
ask for his number, go hang out somewhere or just talk about ur feeling to him
Forget about him, he obviously doesn't like you or he's insecure about something. There are plenty of fish in the sea