As a father who is very involved in my kids’ life, I feel this frequently. At the start of each school year I submit my contact info as the primary contact info and yet sometimes emails will circulate among the class moms anyway. Or I’ll get a text from another kid’s mom asking for my wife’s number so they can plan something.
When we started making friends with parents of my kid, all the moms in the group created a chat group which they still use to this day. The dads didn’t make one because that’s just not a thing you do, and I wasn’t invited to the moms group, even though I knew them at least as well as she did, and I am the extrovert and my wife is the introvert. So I frequently feel lonely and isolated (I also WFH) and my wife is socially overwhelmed.
Yes I could just buck the system and try to get the dads to have a group, or have my wife add me into the moms group, or similar things in other areas of life. But that’s the point: any time I do that I’ll be going against the grain.