Once again, stealth is causing problems in Pathfinder, with the stealth errata adding the following line:
When you start your turn using Stealth, you can leave cover or concealment and remain unobserved as long as you succeed at a Stealth check and end your turn in cover or concealment.
The player believes this means that he can leave cover and attack enemies while remaining stealth.
I believe that from the point you're leaving concealment you're spotted, unless you end your turn in concealment and succeed on a stealth check.
Any help would be greatly appreciated, preferably with as much FAQ, errata and rules rather than logical explanations, since he seems quite resistant to that, but either is fine.