What if somebody tries to make you look uncool and childish?

The key here is to not let this be about someone making you behave in a certain way. Nobody can make you be something you're not. If someone goads you by calling you names, putting you down or suggesting that you're unimportant, it's your reaction that determines whether or not you look "cool and childish". Throwing a tantrum, swearing, getting angry and calling them names would prove to be an uncool, immature response. On the other hand, laughing off the jibes, ignoring the rudeness and staying cool, calm and collected will go a long way to disproving any detractor's attempts to reduce your status.