Is it normal my best friend and i to be this way?

Basically there are times when my best friend basically gets upset with me when I hang out with this girl he doesn't like, but is friends with. She is pretty awesome, although does get a little annoying once in a while and well I met her through him. He acts like he doesn't care, but he doesn't really ask if I hang out with or hung out with anyone else. But when I ask him to hang out basically he says no 98% of the time although he does have a girlfriend and well is one of those people with a million friends.

The dumb thing is that when it comes down to studying all of a sudden he clears his schedule for it and to me it's like you have time to study but no time to hang out. I know school is important, but it annoys me since that's practically the only time we spend together since well we're not as social as we used to be in school. Honestly we're drifting apart and it feels like I'm trying to keep us together. The easiest way to put our friendship is Katy Perry's hot n' cold song. I just don't think the relationship is healthy since we fight a lot, although I admit we still have pretty good conversations when it's just him and me. So is it normal for us to be this way I guess?