Let me review what you've said, in case I misinterpreted any of it.
I stated the group identity replaces and/or subsumes personal identity.
You replied, "How is that personal identity formed, if not by social interaction? I think the dichotomy you refer to is illusory." I believe this indicates that you think all collections of people are "groups" regardless of the way that they formed, the size and any notion of in-group out-group membership status.
So I replied "social interaction != group membership"
To which you replied "I don't think the two are dissociable" which reinforced my understanding of your previous statement -- that you believe all collections of people, regardless of the size or reason for their formation, are interchangeable. A society = team = club = class = mob = airplane full of people = global population = tribe = clan = family = nation = citizenry = company = group = like-working tradesmen = guild = union = etc.
My claim is that this is patently absurd and a remarkably oversimplified model of how the world works, one that's so wrong as to be virtually non-functional. It doesn't provide any workable estimates or cause-effect relationship that apply even trivially across almost any pair of those words. We've decided that these things are so different that we even give them different words, definitions, legal status, philosophies, fields of study, and so on. In fact it's unusual when any of these two words even start to smell like the same thing.
For example, a team doesn't play a game against a tribe, people don't organize labor into a citizenry, a train-car full of people aren't a global population, a nation-state isn't a guild.
These concepts are vastly different and any model that conflates them is so useless as to not be considered.
I believe most of those are social groups, yes. That hardly implies I believe they all work the same way, just that they have some characteristics in common, as social groups.
Most of those "collections of people" lead to certain behaviors, simply from the fact that people self-evaluate and even construct their identity based on their membership and hierarchic position in them.
When you can have a feeling of belonging or not belong, social incentives to reject those not belonging, feelings of pride in your actions as a group, etc, you have a social group, be it a tribe, a company or a family.
Self-categorization theory explains how these groups are formed, and why they are a social group, and not just a random collection of people.
