"Side" means "side dish" or "side order", as in a restaurant, where you might have a portion of meat and a side of some vegetable(s) to go with it. So it metaphorically means a large amount of cynicism accompanied by a portion of cynicism.

At first sight it looks like a mistake, but it isn't. As the author says, it is sarcastic. You would expect a healthy (large) dose of one thing (here cynicism) accompanied by a certain amount of something else (like maybe affection, insecurity, or whatever), but here it is accompanied by more of the same thing (like ordering a main dish of potatoes with a side order of more potatoes). It's a way of saying that you get nothing but cynicism from teenagers: cynicism accompanied by yet more cynicism.

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Note added at 1 day1 hr (2017-07-02 20:19:13 GMT)
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Off topic, but it reminds me of the Spanish proverb "pan con pan, comida de tontos", which means "bread with bread, food for fools". The message is approximately "variety is the spice of life". It's been in the news lately because the Spanish master bakers' association, bizarrely, has petitioned the Spanish Royal Academy to have this proverb abolished.