> How is usage of a private company's private server resources any different?
If you push that argument to the extreme, why should anyone be allowed to publish anything in our county? They can always go someplace else and speak their mind, but we don't want it around here.
What I'm saying is that exists a gradient of power between the dictatorial (state censorship) and inconsequential (your couch), and we have a social contract that allows the same suppression of speech in the latter but disallows it in the former. We call the consequential type "censorship" but it's the same basic action, there is a gray area where private agents working under the authority of the state can be just as powerful censors as the state itself.
For example, if private banks deny services to a newspaper hostile to the government, I could take your argument and spin it around, they are "free" to publish on their own pocket cash, private banks are not forced to "offer a platform". But we clearly understand that publication will lose advertisers, fail commercial and the interests behind the banking ban will have succeeded in suppressing free speech - suggesting them to distribute leaflets will not help.
The cut-off point where private suppression becomes consequential censorship is, in my opinion, when the gatekeepers of speech are centralized and oligopolistic, like for example social media and, unlike for example, traditional print media. A single publication denying publication is perfectly fine, as long as others exists and have reasonable similar access to distributions channels. With the death of traditional print media and the highly concentrated nature of the visual media and internet space, this less the case.
You can of course publish on your blog with zero traffic, but you are effectively shut out of the relevant distribution channels, you are effectively distributing leaflets in your corner of the street.