"There is no provision that requires private companies to do the same. Facebook and Twitter can make arbitrary, irrational, discriminatory, capricious and random decisions about the content they allow. It’s under the auspices of private property rights."
The person with lack of understanding is you.
Neither Facebook or Twitter are private companies.
This has no relation to private property rights in any way shape or form.
Facebook and Twitter are both media companies like newspapers are. Media companies can not "make arbitrary, irrational, discriminatory, capricious and random decisions about the content they allow". By law they can choose what they publish but then be liable to be sued for what they publish or refuse to.
Facebook and Twitter were given special rights protecting them from liability of what they publish to get them off the ground. Given their success, they should no longer special protections not afforded to other media companies.