So far, out of three church services I have attended, in three of them we were instructed by the pastor to shake hands with other members of the congregation, or otherwise greet one another.

If you understand “fellowship” as a meeting among peers, and Christian fellowship as a gathering of Christians to discuss life in Christ, then being instructed to greet one another during fellowship has to seem something like being instructed to greet one another at a dinner party (or super bowl party, or what you will). Imagine:

1. Greet one another.
2. Please be seated.
3. Partake of an hors-de-ouevre and pass along the dish.
4. The weather will be reviewed, and any recent sporting events.
5. Please stand while the main dish is carried to the table.
6. Attendees will discuss their jobs.
7. Praise the cook.
8. Please stand while desert is presented.
9. Praise the cook again.