Zac & The Rock have on-screen chemistry together in the film. There were more like father and son rather than lifeguard partners.
Even though the movie was a comedy...during the first couple of scenes between the two of their characters, Brody was handed everything and never had to work for anything since he won his two gold metals and figured that people automatically had to give his respect & he din't have to work for anything and was basically a show off.
Mitch was getting to him by calling him nicknames throughout the entire film to intimidate him to see how much he could take it; to see how tough he was. Something that goes on in life every.... single.... day! Mitch's nicknames were funny as hell.