Why will Xcode not update?
As a workaround, you can download it directly from Downloads for Apple Developers if you have a (free or paid) account.

Update:  At one time the included link above would take one directly to Downloads for Apple Developers after signing in, however as time goes by things change. So once logged into your Developer account add downloads to the address in the address bar so it shows as https://developer.apple.com/downloads and then press enter.

You should then be at the Downloads for Apple Developers section as shown in the cropped clip below.