It isn't, because it means that a democracy never really existed in Egypt. When a government exists only because the country's military allows it to exist, that is not a democracy. It is a form of military autocratic rule (however benign it might be). It is not unusual for a leader in a democracy to be unpopular, because sometimes they must take actions that many people don't like (but that the leader believes is necessary).
There are ways to deal with the unpopularity of a leader in a democracy. You can oppose his/her actions in the legislative body, or you can oppose those actions in a court of law. You can even seek to impeach that leader if his/her actions are egregious enough. And finally, you can vote the leader out of office in the next scheduled election. But the one thing that cannot happen in a democracy is the removal of a leader by the military, because that action kills the democracy. After all, if the military can remove a leader you don't like, then they also can remove a leader you do like -- which is why all Egyptians should be mourning today, not celebrating.
Obviously, the Egyptian "democracy" was nothing more than an illusion.