XCode update is not being reflected
Unfortunately, I got the same problem some times ago, when, after upgrading to El Capitan, I couldn't update to Xcode 7.1.1.

To solve this issue, I did the following:


Remove the .app file in your Application folder (if you prefer, you can use apps like CleanMyMac to remove any other related files);
Go to Downloads for Apple Developers (after having logged in) and download Xcode 7.2 directly from there.


Don't know exactly why the normal update doesn't work, but now, after re-installing the app completely, everything works fine for me (also the new updates from the App store).