What responsibilty? Can you point to a law that requires Twitter to provide equal access to anyone who wants it and removes their right to free expression? Not just that you think they should, but that they're required to?
Rights are inherent in the US, the 9th and 10th amendments basically say that all rights not assigned to the states or fed are retained by the people. Courts have generally ruled that those rights also belong to "non person entities".
You have the right to punch people in the face but those people have the right to put you in jail and seek civil restitution for it because you infringed on their right to not be punched in the face.
You have a front yard, it's privately owned but publicly accessible property (like Twitter). Your argument can easily be used to say that I should be allowed to put signs in your front yard even if you don't like them there, or what I have to say on them.
If you edit the narrative or others, or censor stories that don't fit in your companies point of view, you are a Publisher and the social media giants should be subject to those restrictions and scrutiny (or something similar).
In Myanmar for example, Facebook IS the internet and the only online source of information - nothing else exists, so by extension, it's true.