We live in a republic with representative democracy. Aside from the initiative system in some states, that is the closest we come to democracy.
In our society, people fetishize democracy. We all want power and the notion of the "people" having the power is a wonderful and desirable thing. What our democracy leaves us is something far different. We get to vote for our own rulers. They are generally members of the ruling elite (e.g., Rahm, Obama, Romney, Clinton, Gingrich, Santorum,etc.), with interests and policies that benefit them at the expense of the rest of us.
CPS had hearings in which parents and teachers expressed their disapproval for closing the schools. Did they ever have an actual vote? Only in their vote for mayor, not for most of the board members, nor for their final decision. The fact that they decided to close the schools betrays their class interests and their disdain for the "people."
Should the board have been chosen by the people? That would seem more fair, but would it have led to any different outcome? San Francisco's school board, which is overwhelmingly progressive and mostly popularly elected just voted to do away with seniority.