First of all, I don't think it's unreasonable to want to keep a bit of independence in a relationship. My boyfriend and I love having our alone time together and going out with mutual friends, but sometimes we do equally go out by ourselves with people that the other one hasn't even met before. As embarrassingly in love as we are, even we do have our own private space sometimes!
However... whilst I understand my boyfriend sometimes wanting to go out for a pint with all of his male friends and not have any women there, I think I'd find it odd if he wanted to go out clubbing without me.
It's an entirely different environment - a lot of people go clubbing to try and pull someone, and it's a place where a lot of groping and flirting goes on. Personally, I hate going clubbing without my boyfriend, as I get hit on quite a bit, and just want him to be there to prove that I don't need or want any extra male attention! Conversely, if he went out clubbing without me, I'm sure he'd get some sort of female attention, and I would find it odd that he actively wanted that. I would expect some part of him to be wishing I was the one there with him, wanting to try it on, and not some random bird!
If he went out clubbing from time to time without me, I wouldn't have a problem. But if he always went out clubbing without me and made it clear I was never going to be invited... that would be deeply worrying. Generally speaking, you go out with your mates without your girlfriend for a pint to talk about blokey stuff. You go out with your mates without your girlfriend to a club to pull other girls.