Trying to reform Islam from Islam's own sources is like playing cards with the Qur'an and Sunna as trumps. Reformers may hold the five, six or seven of trumps (verses of the Qur'an or sayings of Muhammad which appear to support equality and reason) but Islamic religious leaders hold the Ace, King, Queen, Jack, ten, nine and eight of trumps. In such a game, it is the would-be reformers who have the losing hand. Those who seek to promote egalitarian principles from the Qur'an and the Sunna are like a player who keeps announcing 'I have a six of trumps!' or 'I have a seven of trumps!', but what they cannot grasp is that their opponent's hand is full of the highest trump cards.
There is a different game which could be played, in which reasonableness and recognized principles of reciprocity and equality between people are trumps. Such a game could be won by those who want to see change in Islam, for even a 2 in the suit of reason would defeat the Ace and King of Qur'an and Sunna.
The problem is, pious Muslims, true believers in the example and message of Muhammad, will never consent to playing such a game.
Why is this so? The Qur'an puts the matter very clearly:
It is not for any believer, man or woman, when Allah and His Messenger have decreed a matter, to have the choice in the affair. Whosoever disobeys Allah and His Messenger has gone astray into manifest error. (Q33:36)What this is saying is that 'Allah and His Messenger' are trumps. No-one has any power left to choose for themselves once the trump card of the Qur'an and Sunna has been played.
The great difficulty for people in the West is that they cannot comprehend a world in which the Qur'an and Sunna are trumps. They cannot even imagine what such a game looks like. They are convinced that the game is the same no matter what is trumps; that all religions are the same. Worse than this, they are often deceived by Muslims who say that they are playing with reason and tolerance as trumps, but all the while supremacy is given to the Qur'an and the Sunna.
Attaturk well understood this problem, so he forced modern secular values on the people of Turkey. He banned the game where the Qur'an and Sunna are trumps and punished those who tried to play that way. Of course there are many Muslims today who would prefer Attaturk's approach, putting religion in a (very limited) place, and where it could not control public life. However recent decades have not produced a new secularization movement of this kind. In fact the trend has been mostly in the opposite direction with political Islamist movements capturing the hearts and minds of so many of the upcoming generation across the Muslim world.
During the Christian reformation in Europe, protestant reformers did appeal to reason, but their great trump card, which enabled them to win much of Europe to their cause, was the Bible. They declared that the Bible trumped church tradition, and this made all the difference.
The challenge for Islamic reform is that making the Qur'an and Sunna trumps just takes the world back to sharia law.
And this is very bad news for the women of Islam.
 The Sunna is the teaching and example of Muhammad. This is held up as having canonical authority in determining Islamic law.
 For those who do not play cards, here is my attempt to explain. In many card games, higher cards 'beat' lower cards. Ace is highest, then King, then Queen, then Jack, then 10 down to 2. However if one 'suit' is declared 'trumps', then it beats all other cards. E.g. if Hearts are trumps, then a 2 of Hearts (the lowest Heart) beats all Clubs, Spaces and Diamonds. The Ace of trumps will be the highest card of all, and will beat all other cards, including all the other trump cards. The choice of trumps determines who wins the game.