Free speech is a protection from the government interfering with your right to express your opinions. Youtube is not a government.
My megaphone belongs to me. Do I have the right to limit when and how you can use it? Do I have the right to refuse to let you use it? Yes, it is my property. Youtube is somebody’s property. It is not an instrument of government.
No one made that argument.
"Youtube is somebody’s property. It is not an instrument of government."
Except, I'm not sure that's true anymore unfortunately. Same goes for Twitter.