No one here made that argument. At this point, I'm not sure you even remember what the argument is. Let me roll this all back a bit to the Marsh v Alabama case:
The court pointed out that the more an owner opens his property up to the public in general, the more his rights are circumscribed by the statutory and constitutional rights of those who are invited in.
In its conclusion, the Court stated that it was essentially weighing the rights of property owners against the rights of citizens to enjoy freedom of press and religion. The Court noted that the rights of citizens under the Bill of Rights occupy a preferred position. Accordingly, the Court held that the property rights of a private entity are not sufficient to justify the restriction of a community of citizens' fundamental rights and liberties.
As you can see, it doesn't matter if a private entity declares private ownership. When you open your private area to more and more people, then those people's rights quickly begin to supersede your own. Cases such as this is also why businesses can't just ban people for being black, gay, or muslim. As you open your business more and more to the public, your rights as a private business end as the rights of the customers begin. I'm surprised you're siding with the corporations on this one, Dave. I always thought of you as a more left-leaning fellow. Should Twitter be able to ban people for any reason?
Businesses can't ban people for being black, gay, or muslim because those are protected classes in anti-discrimitory law. Which didn't always exist. Remember the time blacks were banned from certain businesses?
And even IF you want to apply the first amendment to a private business, again, the first amendment clearly states that Congress shall make no law restricting it. It says nothing about a private entity not being allowed to restrict freedom of speech.
The rights of the customers never ended. Why would you think they did? The problem, I think, is that you see the first amendment as applying to everyone even though it very clearly states that it only applies to congress. (ie. congress can't limit free speech)
As for why:
Honestly? I hate idiots. Meme spreaders. Fake news. I'd rather Facebook and Twitter and all social media crack down and ban those people than watch as society crumbles into shouting matches of emojis and images with vague, nationalistic or misleading messages.