Is it normal to not tell someone things

Depends what it is. If he doesnt want to tell you something because it is between him and someone else, then he is respecting the other persons wishes, the same way you would expect him to respect yours if you ever told him anything. I'm sure if your best friend told you to keep a huge secret for her, you would and you would try not to tell your bf unless it was he's business in any way.

But if it is about he's own life and it is affectig himm, then he should be able to tell you. After all being open wih no major secrets is the best way forward.

That would piss me off. What an ass. Tell him it's a two way street and only assholes keep things from their girlfriends.

if you have been going out for a long time then you don't have to tell each other EVERYTHING but there shouldn't be things that he CAN'T tell you he should trust you enough to being able to tell you..
but if you haven't been going out that much then give it time.. maybe he'll tell you later on..

you also dont have to tell him everything

you can tell him your personal stuff but he won't tell you his personal stuff?
Try to work on this trust thing.

Oh yes! It is quite normal.