Cosimo has now met my dissertation director and I've met his. It feels like bringing someone home to meet the parents--except with a less clear script and a less clear sense of what the introduction is meant to accomplish.
When you take a new partner home to meet your actual parents, you're facilitating an introduction of people who might conceivably wind up stuck with each other for decades; even if they see each other only infrequently, the two parties will play a continuing role in each others' imaginative lives for as long as each is associated with you.
The same, presumably, is not true of the advisor/advisee relationship. Yes, my advisor is one of my most important intellectual influences, and yes, Cosimo is in an adjacent subfield and might have had a distant professional interest in meeting her (or she in meeting him). But it wasn't about anyone's intellectual or professional life--or if it was, it was about that weird space in which the intellectual and the emotional overlap and are indistinguishable from each other.
I spend a lot of time in that space. And in it, my advisor is mother, father, and both sets of grandparents.