I think the confusion stems from the fact that most people speak through or on private property—both digital and physical.

But they're taught in school that there is a general "freedom of speech" which doesn't really exist. This sentiment is echoed in mass American media to adults.

There's very little "public" speech in a legal sense. The most populated speech structures are privately owned. Censorship is built into those structures. America, as a whole, does not have "free speech" except for property owners. Unless you're on public property, behaving lawfully, such as in court, or "speaking truth" next to the post office, etc. etc. you don't have free speech.

So, when people hold a good portion of their discourse through private structures, those structures seem public. The host companies seem like governments through terms of services. They see the first amendment as applying there by default.