You are missing a key factor in Egypt... they are sort of in a state of emergency right now, so it’s not unusual for any government to suspend certain rights for the duration of the emergency.
The country has effectively always been in a "state of emergency" ever since the late-1960s which is how a constitutional republic and a democracy can get away with trampling on the masses.
Incidentally, the president of Egypt just dismissed his cabinet, but plans to stay in power. It's a compromise, but is it enough to quell the masses?
(And I'll say I'm impressed with the progress these popular uprisings have had, I was expecting a repeat of the unsuccesful actions in Iran last year, where the government holds on to the policy/army/paramilitary and so doesn't go anywhere).