When it does that just sign him out. Then it will go to a sign in screen with his name and password filled in because likely if you look at the boxes, it is checked to sign him in automatically. Unclick that. Now sign up for your account and don't click to auto sign you in. Now when each of you go to sign in it will be blank and you fill in the info for the person that wants to sign on.
Clear as mud? Sorry. Hope I explained it.