Remember what is the role of the army and security forces; it is to protect the interests of the power structure against the population. While that makes them dangerous, it does not make them the authority.
The real fight can not be against them, and to destroy them (even if you could) would leave legitimate authority defenseless once it is established. You do need an army.
If you were able to eliminate the army, Egypt will simply be invaded by hired private mercenaries like Blackwater, Erinys, and G4S, who will be even more vicious and better trained. (Incidentally, there is already a large presence of these security companies in Egypt preparing exactly for that eventuality).