Why would this guy always ask me out and then claim to be 'busy' once that day came?

He might really want to start something serious with you but I think he is kinda playing the hard to get game. Don't stop talking to him otherwise your not be able to know what his intentions truly are. So keep things loose and wait for him to ask you out again. And wait in the last minute and tell him that you are busy. do that two times as he did and see what his next move gonna be.