Let's get this straight right now; that is not what free speech means. The very first words of the First Amendment are "Congress shall make no law ..." You will note that those words explicitly mean that this does not apply to people or corporations (because corporations are people too). So a corporation doesn't have to give people a voice, even if it's in the business of providing voices, and it can censor those voices however it wants. The First Amendment argument only really has a place when it's the government which is restricting speech - such as the FCC slapping down fines on people. Why do people think this is the case? It's a misunderstand, sure, but there has to be a reason that so many people seem to misinterpret the law.
It might be a sense of entitlement. In this country, we have it hammered into our heads that we can say anything we want, short of a "clear and present danger" or defamation. But because of various technological advances, a huge majority of our speech is mediated by corporations. For me to make this blog post requires the use of a computer (made by HP), OS (made by Microsoft), blogging software (made by Google), and internet access (provided by Charter). At any point in that chain, there is an opportunity for censorship, because none of those corporations has any legal requirement to allow me to do what I want - in fact, I have "signed" contracts all of them, even if most of those were click-through EULAs that I didn't actually read.
The other reason might be that it doesn't happen all that often. People then assume that because it's not happening, it must be illegal. There is then the question of why it's not happening, and I have a few theories about that:
1) Restricting speech is bad for business.
If Company A restricts speech and Company B doesn't, people will be more likely to go take their content creation to Company B. While speech restriction might raise the overall quality of Company A's offerings, overall quality is pretty unimportant in the era of search. There are also a few (weak) legal grounds on which to sue Company A - misrepresentation and discrimination being the big two.
2) Restricting speech is damned expensive.
This is one of the things that always bothered me about 1984. Who is watching all of these people? It would take a huge amount of workers to police even a small slice of the content output of the internet, and it would be brutally inefficient to boot. In the future, this job will probably be handled by artificial intelligence - already there are algorithms that can pick out "content of note", but those are mostly used by our intelligence and advertising agencies.
3) Restricting speech happens, but it happens to people who aren't sympathetic.
There are certainly examples of this happening. This is why there aren't nude pictures on Facebook or graphic videos on Youtube. In those circumstances though, the company in question looks good, because they're removing something that most people don't want to see when they go to those places. In other words, it doesn't look self-serving. More problematic is the issue of copyrighted videos, which Youtube will remove even if they fall under fair use (though this is still its prerogative).
Of those three, I think that the second one makes the biggest impact. As time goes on, bots will get better at tagging objectionable posts for human review. They'll need to do this for all the stuff you're not allowed to put on any kind of commercial site, both of the "clear and present danger" type and the porno/graphic type. This is especially true now that the scepter of cyberbullying has been raised. As the technology gets better, the temptation will grow to turn it on whatever kind of speech hurts the corporate bottom line. This is especially true if, like Apple, you have the infrastructure set up to go through content by hand, one at a time.