The confrontations in Egypt are perhaps all the more dangerous because both sides claim — and I suspect believe sincerely —that they are on the side of democracy. President Morsi's supporters (the Muslim Brotherhood and others) see him as duly elected, and taking a stand against an entrenched bureaucracy and judiciary, much of which consists of Mubarak era "remnants." In fact, I suspect some of Morsi's moves are widely popular: firing the hated State Prosecutor,blocking the courts from dissolving elected institutions like the Shura Council, etc.
But his decree went beyond blocking the courts from interfering with elected institutions, giving himself powers with no oversight whatsoever. The overreach is the problem. And the Brotherhood, while correctly noting Morsi won an election, overlooks the fact that he did so with 51% of the vote (and got less than 25% in the first round. Not a huge mandate.)
His opponents, however, must recognize that while he has overreached, he does have a legitimacy they were unable to achieve at the polls.
If one side is taking a straight majoritarian approach to democracy: we won, so we get to make the rules; then the other side is taking the approach of denying him any legitimacy despite his electoral victory.
The problem is that democracy requires, , if it is to function properly, both the rule of the majority and a protection of the rights of the minority. The polarization in Egypt (which reflects a polarization of society) excludes any room for negotiation and compromise (so far), with even "liberals" like Mohamed ElBaradei speaking of non-negotiable demands. It's the problem of the excluded middle: both sides see democracy as a zero-sum game. (The fact that many of these statements could also be applied to the "fiscal cliff" discussions in the US Congress at the moment is purely coincidental.)
It's time both sides stepped back a bit and remembered that if the polarized sides do not find a way to work within a democratic frame, someone else, perhaps someone in uniform, will perhaps feel obliged to act.