People have a right to speak their mind. But that doesn't mean others must give them a platform.

That is not entirely a true legal statement. I am not a lawyer, but others have put forward certain arguments like Water companies, Electricity companies, Telecommunication companies, and other things legally deemed "providers" are actually disallowed from censoring any opinion at all, ever. But in return, they are provided with immunity from prosecution, so they also cannot ever be held responsible for anything anyone uses their services for.

This is where Twitter is currently in potential legal trouble. On one hand, they are requesting from Governments the legal immunity clause, saying they can't possibly censor things people put on their site, it's an unsolvable problem. Everyone agrees with this statement, 7 billion people tweeting every day cannot be moderated by humans or machines. But then if Twitter claims it is a provider, then it must stop censoring anything on it's platform. They're trying to get the best of both worlds, and iirc they are currently involved in a few court cases over it, as well as YouTube.