Not only did he make it up, but it is false! Multiple lines of evidence point to a O(n log(n)) law instead.
https://www-users.cse.umn.edu/~odlyzko/doc/metcalfe.pdf has the details.
https://www-users.cse.umn.edu/~odlyzko/doc/metcalfe.pdf has the details.
> In general, connections are not used with the same intensity... so assigning equal value to them is not justified. This is the basic objection to Metcalfe’s Law...
In my architectonic opinion, the perfect network comprises all nodes operating equally. Ergo the ideal is indeed Metcalfe's law, but architecture and design can be costly, which is simple the inefficient use of resources. These being very precise machines, anything less than 99.999% is amateur, ergo the law obtains.