Private censorship is absolutely censorship. Anyone disagreeing is engaged in a dishonest semantic argument as there are numerous examples of it usage this way that predate this debate by decades.

The argument is that the first ammendment protects the right to engage in private censorship.

In my mind, the core debate at the center of the issue is the assertion that corporations have the same rights as any other citizen. I think that is patently absurd but the Supreme Court disagrees.