Calling people old: the experience of a 30yo around people in their 20s

I'm getting my second Master's degree in Germany right now, and due to that I am around a fair amount of people in their 20s (uni setting). Recently I've put together an interesting thing about being called old, and the fear of aging.

My best friend here is a 23 year old Ukrainian woman, who's lovely, academically-oriented, etc. She's never once called me old, or really referred to my age at all (with the exception of asking for "big sister" advice). We have a 7-year difference, and that literally never comes up. We just interact like peers.

But then, recently I've made a friend from Greece, who's 26. Now, in the 3 months I've known her, she's called me "old" 3 times. Twice in front of others. So, once a month on average, she calls me old, laughs, and I have to chuckle along. We have a 4-year difference. But she can't get enough of making it clear that I am old, and she is not. Both born in the 90s, and I hadn't even started kindergarten when she was born. Yet, I'm a withered grandma in her eyes.

Through this experience, I realized that the need to repeatedly call someone old is just an expression of your own fear of aging. My Ukrainian friend doesn't rub it in because she hasn't had that "reaching 30" fear set in yet, but my Greek friend is staring down the barrel. And this is where this rude behavior stems from. That's my theory anyway.

It's comforting, in a way. Now, the next time she or anyone calls me old, I can just chuckle because they're really just outing their own fear of aging. We can say "yes I know aging is scary lol, sorry time passes for you too ✌️"

Does anyone have thoughts or experiences with this? Does my theory hold up?