This is a wonderful video of a speech given by Gamal Abdel Nasser in which he recounts a meeting with the General Guide of the Muslim Brotherhood (at the time, probably Hassan al-Hudaibi) in which he tried to patch things up and, as he puts it, "set them in the right direction." He asks them what their demands are. The Guide replies that his first demand is that all women in Egypt be forced to wear the veil.
The interesting thing is that this line generates an uproar of laughter in the audience. One man shouts out, "why doesn't he veil himself."
With very dead-pan delivery Nasser continues. He says that he doesn't believe that this should be imposed on anyone, that it's a personal choice. The Guide insists, telling him that he should, as ruler, impose the veil. Nasser then relates that he replied: "Your daughter is studying medicine. She does not wear the veil. If you can't impose the veil on your daughter, what makes you think I can impose the veil on 10 million Egyptian women?"
The depressing thing is that, back then, you could mock the leader of an Islamist movement for wanting to impose an alleged religious duty. Today it seems it would trigger anti-blasphemy lawsuits.
Of course Nasser may be at least partly making this up. Although close to the Brothers before he assumed powers, and fully sharing their authoritarian streak, by the time he made this speech he was repressing them. It may have been convenient to ridicule them. But it's the audience reaction that is the most telling.