And a core fundamental principle of property rights is the right to exclude.
For example, the right to exclude certain classes of people is different renting a room of your house vs. renting a whole apartment.
The ability to exclude is again different for service providers. It sometimes also depends on their size. e.g. larger banks are obliged to provide a free basic bank account.
If social media monopolies are seen as excluding people without good reason, their monopoly status might attract attention for regulation in the same manner.
The damages in this case are more abstract, but Facebook arguably has cause to exclude. That said I am much more open to debate the merits of this particular exclusion rather than whether Facebook can exclude at all.
I’m also going to go out in a limb and point out that Facebook does not in fact have a social media monopoly, certainly not in the United States which would be the jurisdiction here because in order for that to be true, everything from Twitter, TikTok and iMessage to WeChat and YouTube and Snapchat would simply have to not exist.
Social networks tend to have overlapping user bases, with people on both Facebook and Twitter, or Facebook and Snapchat, or some other combination. Nobody has yet convinced me where and how Facebook has any sort of monopoly because they’re too focused on the large user base and that in itself is just not a good argument. Feel free to take a stab at it though.