There's a significant difference between private enterprise and government. For example, no matter how much a business doesn't like you, they can't jail you based on their own set of rules (laws).
If there are not other bars to go to, and if instead of bars we're talking about vital services such as food, housing, or communication that have been monopolized or oligopolized, then that assumption no longer holds.
I don't think Twitter itself is anywhere near that type of critical. But in general it's ignorant to write off "private enterprise" as if it something that is entirely distinct from "government". And this goes doubly in the US where "private enterprise" ends up shaping much of society.
If an argument about vital services is to be applied, I think it is much better applied to something more foundational to the internet, such as domain name registrars or ISPs.
I am pointing out that if we view freedom of speech/association as a natural/human right, it is possible for entiti(es) that are not the bona fide "government" to be oppressing that right.
This is trivially demonstrable by interpreting any existing society as an anarcho-capitalist paradise where there is no government, just one large company you're forced to contract with to obtain vital necessities.
For a real world example within our society, take a look at the list of songs censored by Clear Channel in the wake of September 11, 2001. There was no bona fide government edict declaring this, just opaque corporate power ultimately wielded by the same people marching us to war in most other forums.