Unity without fellowship

Crowds exhibit deceptive unity. Take a crowd at a public fireworks display. The crowd is united in the sense that everyone came to see the fireworks display. However, once the spectacle is over, the patterns of crowd dispersal expose how deeply disunited the crowd ultimately was. When it disperses, the crowd typically breaks up into smaller groups consisting of romantic/married couples, friends, and family. Separate little groups whose members are united with each other through bonds of emotional affinity. But there's no affinity between groups, beyond the temporary affinity of the spectacle they came to see. 

They don't leave as a group. They don't leave as a unit. Rather, the groups comprising the crowd go their separate ways. They may never see each other again. 

And after the crowd has dispersed, there may be one person left, standing alone in the deserted park where the throng was an hour before. A street kid. An orphan or runaway. He belongs to no one. Has no one to go home with because he has no one to go home to. He was briefly part of the crowd but the crowd was never part of him. There were hordes of people around him, but when they vacate the area, he was left behind and left alone. In a deeper sense, he was always by himself, even when he was in the middle of the throng. 

Catholic apologists love to quote Jn 17:21, but Catholic unity is fundamentally external. A structural unity of papacy, episcopate, and priesthood. As well as unity in the sense that observant Catholics take the same sacraments. 

But it's unity without fellowship. Although a subset of Catholics share the same beliefs, that's not a sine qua non of Catholic unity, which is fundamentally impersonal and external. 

It's like the anonymous crowd that gathers to watch a fireworks display. All the crowd has in common is that fleeting interest. The unity of the crowd was just a shell temporarily housing random individuals.