Mr Orange shouldn't have told Mr White he was a policeman
What did it accomplish? White may or may not have killed him because of it. White got gunned down by police officers. He went to his grave a broken and devastated man because his young apprentice betrayed him. Hell, if Orange didn't say anything, I think White would have surrendered to the police and lived. He may well have died in prison but I'm sure Orange could have pulled a favour or two for him.
It was just an all around bad thing to say given the circumstances.