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I'm talking about a shared private/public key for everyone which gets changed when members leave or enter.

What are you imagining a "shared private/public key" is ? Because that's not a thing.

A private key is _private_, it doesn't mean anything to share one of those, if you're doing that it isn't a private key any more and you wasted your time.

They probably mean a single symmetric key shared between all. And private is not mean that only one person knows a thing. Quite the opposite. If the entire planet minus 1 person knows something, that's a form of private as well. Either way you're arguing semantics.

A shared key would allow impersonation/spoofing within the group.

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