Not participating in politics, getting releaved from the economic burden of sustaining the househld (at least normatively) does not bother Egyptian women as much as not particpating in boxing matches. This is the problem; those most concerned do not demand such rights. Women themselves have become fierce agents of consolidating such ideas and even implementing them. It is not a structural problem that hiders thier entry into the political scene. Conversely, sucess in the political sphere is determined by other factors.The structure could be hindering all different serious parties, if there is any. In fact some women can make it through the existing structure. I don't see it as a political problem at all. Women's issues  are only a mainfestation of a political struggle  between the secular oriented regimes and the Islamic movments. 

It is a cultural problem. 

Most Importantly, don't tell me that Egyptian secularists are" really" supportive women's rights. Most of them are hpocrytes. , as Lama Abu Auda hinted. Instead of wanting to cover women up in the public space, reducing women to their bodies under the assumption they are a commodity, they would like to take thier clothes off to enjoy thier bodies,also as commodoties (except for thier wives, daughters and relatives of course).  You are so optemestic