Basically: when you use a certain variety*, you're signalling your group identity. For something like "six seven" that's immediately obvious — it doesn't convey anything on its own, only that identity.

You don't get the opportunity to use the word "shibboleth" often, but this is one.

I think there is also another thing where the fence you erect by choosing another variety is not necessarily between you and someone else, but between you and yourself. This is something I notice in myself and my sister. We are both introverted and uncomfortable sharing personal feelings and emotions - her especially. And she has a strong tendency to express emotions in English and not her native language. I think the added abstraction acts as something of a shield, making the sharing feel less personal and thus less scary.

I used to write poetry and I experienced the same thing there. I had a hard time writing poetry in my native tongue as it felt too personal, so I only ever wrote in English and French.