'Big mad' is emphasised slang for 'very angry' — often used mockingly, as in 'why are you big mad?' meaning 'why are you taking this so seriously?'. The phrase implies the anger is disproportionate. If your teen accuses you (or a friend) of being big mad, they are saying the reaction is over the top. Slightly cheeky; can be irritating in arguments because it dismisses the other person's feelings.