Egypt: the "coup" is product of the popular revolution, not the other way around

image from WG

Let my stand on this matter be absolutely clear: regardless of whatever contacts and interactions between the actors involved, when millions walk out persistently in demand of change it cannot be caused by any single nor composite socio-political force but it responds to the real demands, anger and outrage of the People. In Egypt as in Turkey, Brazil or anywhere else.

Another thing is where the processes triggered by such a human tsunami leads to. Probably nowhere without a socialist alternative that can fulfill the popular demands of "bread, freedom and social justice", and this alternative seems so far not in the menu. 

But in any case:

1. Morsi was ruling almost illegally: when the Supreme Court annulled the Parliamentary and Constitutional Assembly elections (on quite good grounds), he did not obey and call new elections, obviously fearing that their pool position advantage (tolerated by Mubarak, sponsored by Saudi Arabia) had been already very eroded.
2. Critically, Morsi was ruling illegitimately, just as Rajoy does in Spain or Erdogan in Turkey. When you do not have the backing of a clear majority anymore, you must put your power at the disposition of the People, calling new elections. It is not and never will be legitimate to stay in power when popular support wanes in such dramatic manner. No matter what laws and constitutions say, they should say otherwise. 
3. Morsi has been an obedient puppet of the USA and its main regional allies, Israel and Saudi Arabia. Against the clear will of the Egyptian People he did not even open the border with Gaza in order to alleviate the Zionist siege and he has played always in favor of the Capitalist system of exploitation and therefore has not been able or even willing to solve the dire problems of the Egyptians, which cannot be solved in a Capitalist frame, be it fundamentalist or secular, authoritarian or pseudo-democratic. 
4. The Egyptian Army is highly dependent on US subsidies, being (with Israel and Colombia) one of the top beneficiaries of US military aid. The reason is obvious: the canals (Suez Canal in this case), as well as Egypt being a major regional power, at least potentially. Therefore we should not expect it to bite the hand that feeds them: their main interest is the stability within the Western-Capitalist imperial order, as that is what their master commands. Therefore their intervention is clearly intended to canalize the protests to a stable outcome and nothing else. 
5. Similarly the Muslim Brotherhood is highly dependent on financing by Saudi Arabia and other Arab tyrannies and therefore they will negotiate their place in the new system, knowing that they still have many supporters which will grant them a place under the sun in the new parliament and maybe government. If they do otherwise they will surely fragment and become quite irrelevant. 

The only one who is not dependent on foreign subsidies is the Egyptian Working People. Their demands are clear: bread, freedom and social justice. Will they be met by the new government? I doubt it but only time will tell.