It is an easy thing to manipulate events and public opinion, especially when powerful institutions like the army and media are collaborating together on one particular project or have their eye on a single goal. This has always been true in history, and it is true today, in any country, and under any political system, democratic or authoritarian, Western or Eastern.
But, with that said, saying that the Egyptian army hatched a grand political conspiracy to bring millions of Egyptians to the streets and then exploit their massive anger and frustration to fulfill their original goal of removing Morsi from power is too hard to believe even for a diehard conspiracy theorist. Anyone who has been paying attention to events in Egypt prior to this crisis knows that the people were fed up with Morsi's presidency, and did not trust him with the key to the treasures of the country.
If Morsi had played it smart, if he had humbled himself before the revolutionary street, and recognized the demands of the millions of demonstrators, such as agreeing to hold early presidential elections, then he would've diffused the legitimacy crisis that was surrounding his administration. He could've cut the army off at the knees politically, in the field of public opinion, and prevented it from making any move against his rule.
But, the nature of the Muslim Brotherhood is anti-democratic. It is anti-public opinion, as Egyptian journalist Yasser Rizq points out in this article. He says the Muslim Brotherhood considers the people to be a herd, and that their opinion doesn't count. They do not respect the voice of the people, they do not even think it is a power to be dealt with, but a nuisance at best.
That view is not unique to the Muslim Brotherhood. But the problem with holding this perspective is that the Muslim Brotherhood doesn't have any force or power in Egyptian society on its side; not the state media, not the army, and not the people. It has various volunteer militias and terrorist groups, but terror alone can't move a society towards a desired direction.
Morsi put himself in a box by not pursuing consensus politics. He instead tried to transform Egypt, and even attempted to use its nationalist army to intervene in Syria. Egyptians weren't deceived.
To say the ousting of Morsi was a defeat for democracy is crazy and illogical. Morsi abandoned democratic principles the moment he won the election. He sought to consolidate power during his brief time in the sun, and it backfired.
A charismatic revolutionary figure or a powerful general who has the loyalty of his soldiers and the respect of the nation can get away with a lot of things that Morsi did not. Morsi, an ideologue from a political party that has been historically defiant towards Egyptian public opinion, and uses tactics like terrorism and assassination to achieve its religious and political goals, never had a chance to transform and dominate Egypt.
Remember, Morsi is a man who said that Jews are the "descendants of apes and pigs" - this statement disgraced his intellect and his character, this alone should've sealed his political fate.
Morsi is obviously not someone who is attuned to the popular moods and sentiments of the age, either culturally, religiously, or politically, either in his own nation or internationally. It is a problem when as a leader of a historic nation you make silly and racist statements because you don't care what people think about you. Morsi was not at all sensitive to Egyptian public opinion and he paid the price.
To grieve about Morsi's overthrow by the army because he was Egypt's "first democratically elected leader," as many pro-democracy liberals are doing, is both stupid and shallow. "Democratically-elected leader" means nothing in this case because over 60 percent of the Egyptian population did not vote in the presidential election in 2012. They expressed their will through street protests and petitions.
Elections are not the end and be all of democracy. Imagine if a donkey, or a medically certified insane person, was elected president, would you still defend the system of democracy then? Democracy, as it is practiced today in the world, belongs in the dustbin of history, not on a pedestal.