Someone is getting a big dick when they try to prevent you from doing something you really want to do, when they get heavily angered/saddened at something small, or a mixture of both.
Person 1: "I need to leave work 30 minutes early tomorrow."
Person 2: "No. I don't give random breaks to my employees, who the hell do you think you are?"
Person 1: "Don't get such a big dick about it."
Person 1 to Person 3: "Wow, our boss was getting a big dick earlier."