I don't want to defend Rouhani, because I disagree with him. But I don't think he's quite the monster people are making him out to be here, so perhaps I can provide a context to his point of view.
The idea of freedom of speech is very non-intuitive. If it's not a value instilled in you by your culture, you're going to have a difficult time accepting it. Many people have died, and continue to die, for the West to gain and protect this right, from Socrates in ancient Greece to the Charlie Hebdo cartoonists in Paris. If there's anything worth considering as sacred in secular culture, I think it's the right to speak your mind even if it offends others. But this moral truth is not obvious, and it's taken a long time for Western society to really accept it. Less than three hundred years ago people were still being burned at the stake for heresy in Europe. And even now there are Western politicians who question the separation of church and state.
The Eastern cultures have largely not had the same experience. Even if once there had been civilizations with more open societies there, the memory has been lost to the social consciousness for one reason or another. Some ninety-year-old semi-literate Ayatollah in Iran can not conceive of a society where anyone can insult his sacred beliefs. He has not studied the history of the French revolution, the idea of tolerance of what offends you is too abstract for him, and he is suspicious of any values not handed down to him by his particular culture. He's too old to change at this point. Unfortunately those Ayatollahs are in charge of Iran. They are not all horrible people. Some of them are kind-hearted, some are brilliant, some are ignorant and cruel. Almost all of them are too old to change their minds about totally foreign concepts like absolute free speech.
Rouhani was born in a religious family in some tiny desert town of 10k people so isolated that it has its own language, and yet he received his PhD from a university in Glasgow. He's 67 years old. He's already changed as much as you can expect a human being to change in one lifetime. The world he was born in has gone through several seismic shifts under his feet. It's experienced a massive revolution, complete social upheaval, a long bloody war, sanctions and global isolation, and now yet another major transformation, and for all of that he has been near the epicenter. He has kept up with it as much as you could expect, and yet that world is still changing just as fast.
Iran is a country where two-thirds of the population is under thirty-five, but where the oldest stratum of society rules the place. There are eighty and ninety year-olds who are too senile and inflexible to change their minds about anything, but who are deciding and legislating acceptable social behaviour. The younger generation is worlds apart. They may not all have had equal exposure to modern Western culture, but thanks to global media, the internet, and the shrinking global cultural space, they have far more access to it than their parents and grandparents ever did. As a result of these demographic and cultural shifts, an inevitable sea-change is about to take place that will fundamentally alter Iranian society. But it is going to take a little bit more time. The older generation will not and to a large extent can not keep up with the pace of change. It only makes sense to allow for a graceful transition.
I disagree with Rouhani's stance on free speech, and just about every other young Iranian I know does as well. He's a member of the ruling class, and has not felt the political suffocation we have felt our entire lives. He has not experienced the bitter irony of being unable to admit in public what you believe or don't believe in, while being bombarded with propaganda that celebrates the liberation of Iran, before you were born, from some despotic monarch who apparently did not let people speak their minds.
At the same time, Rouhani is far more progressive than those 90-year-old Ayatollahs obsessed with appropriate Islamic clothing and the presence of women in soccer stadiums. I deeply disagree with his stance on free speech, but I understand that the older generation he represents can not conceive of the Iran I believe is possible and in fact inevitable.
I would love to tell him to shove his religious rules and holy book somewhere dark and damp. It would be unbelievably cathartic to me, and I should have the right to be able to do it. But I think right now it's not the right thing to do. He is beginning to lead the country towards the right direction. He can't immediately transform it to Scandinavia. Iranian society is not quite ready for that. It has to happen slowly and gently in order to avoid cultural ruptures between the different strata of society, young and old, secular and religious, urban and rural. We have to avoid the kind of cultural clash that contributed to the 1979 revolution.
Meanwhile, what we can do is keep the conversation going. The fact that Rouhani is even mentioning free speech and its possible limits at all is going to make it a topic of conversation in the most conservative part of Iranian society, where that concept is most foreign, in a way that I could never do. I have hope that something positive will come from that. He's expressing a sentiment I disagree with, but a few years ago he wouldn't have to say it at all.