The most sensible response comes from a non-native speaker:
'My mother, my wife, my children, my students. I don’t think “my” in this context implies possession, to me it implies a relationship. It becomes even clearer when talking about “my employer”. But I’m not native, does this have connotations I’m unaware of?'
No, it doesn't. It's just that you're dealing with a bunch of idiots.