Not waving but drowning
The hardest (oddest?) part? You learn that a fairly likely outcome of your attempt to rescue a conscious non-swimmer is that you will be attacked, and so you have to learn underwater combat tactics, so that you won't be drowned the first time you try to carry out a rescue.
infinite intimation and other former lifeguards comment in the Spot the Drowning Child thread, while some survivors remember. Plus, Mefi's worst (imaginary) lifeguard, racial swimming disparity / swimming pool discrimination, dreaming underwater, and PS: Please don't throw babies in pools.