They are lying or brainwashed. Progressive ideology (which is actually Westernised neomarxism) spreads through academia, which is
extremely biased to the left. Academics exploit young students' naivety, gullibility and recklessness to impose their progressive political beliefs onto them and to turn a smaller number of them into political activists like you see in these protests.
Over time they gain total control of this institution, and when that happens a new phase begins. In Turkey this hasn't happened yet but you can see it already in the US and many other Western countries. In those countries, now that the progressives have total control of academia, speech that goes against progressive dogma is not allowed, not even by tenured professors, and in many universities if students want to get their degree they must complete mandatory courses where they accept progressive political ideology. These are the same people that used to call themselves "liberals" and pretended to care about freedom of expression - now that they're in total control, they don't allow anyone to say or do anything against them or their cancerous progressive ideology. These students' cries about free speech are nothing but rhetoric, even if some of the students themselves believe it (most are just pawns).
In much of the West this ideology has already spread from academia and taken over the media, corporate management, Big Tech, HR, administration, much of government, and even subcultures like knitting. Make no mistake, its end goal, explicitly stated in the academic literature it comes from, is to
dismantle society and replace it (with them in power, ofcourse) through the same type of
cultural revolution that happened in China.
Personally I'm not religious and I dislike authoritarianism, but everyone, including these students, would agree that there are some things that should not be allowed in a society. An ideology whose goal is to dismantle society and remake it into a totalitarian woke hellhole should absolutely be one of those things. And that's exactly what this is, no matter what they claim, no matter what lies or delusions they use to conceal this fact.