+2  A: 

You need to set the permissions of the subsite to not inherit from the parent. This is an option when you create the site. To stop inheriting permissions on an existing site, go to:

Site Actions -> Site Settings -> Advanced Permissions -> Actions -> Edit Permissions

Then you can set who has access to the subsite. A user with no permissions in the subsite will not see the tab.

It's all explained here.

Andrew Strong
@Andrew - Good Answer - Might have explained that even after site provisioning, you can break permission inheritance and set permissions as needed. +1 @Ahmad - OOB, MOSS2007 implements Security Trimming. That is to say, "Users can't see items/lists/libraries/sites they do not have access to." You should mark Andrew's answer as the correct answer.
AdamBT
@AdamBT: Isn't the decision for correct answer up to @Ahmad?
Alex Angas
Thanks a lot. I found the place where I can choose that when creating a new site (unique permissions) but where can I edit and change those of the one which is already made?
Ahmad Farid
Answer updated, it's actually in a pretty easy spot to miss.
Andrew Strong
Thanks man for all the effort. However, I was not able to edit permission if the site inherits from the parent one so I made a new one with unique permissions. Best wishes :)
Ahmad Farid
@Alex - It was just a suggestion. Andrew gave the correct answer and I was just confirming it for Ahmad and other users that might have the same question. I said "should" not "you have to" for the benefit of the community. I get nothing out of it whether it is marked as the answer or not.
AdamBT
@Ahmad - If you have admin privs, you should be able to break inheritance and set the permissions as needed. See Andrew's edited answer.
AdamBT