Why should your agar plate not be incubated at 37C?

Generally the reason is that that's the temperature of the human body and there's a chance you'd accidentally grow something that could be pathogenic to humans, which you don't want because if you don't realise and accidentally inhale it, you'd be inhaling fully grown, mature, most likely infectious micro-organisms, all ready to land you with a nasty illness. It's basically just a health and safety precaution, at lower temperatures, the organisms grown are less likely to be adapted to survive in your body, so if they are inhaled or gain entry to your body somehow, they won't likely last long.