Sharing Apple Airtag with family: Unable to share AirTag

I am trying to share my AirTag. I followed the Apple Support document Share an AirTag or other item in Find My on iPhone and updated my iOS as indicated in an answer for How to share an AirTag with family members . I have the option of adding people, but when I click it, I get to choose a contact. When I chose the person, who has an even newer iPhone than mine, it says, "**unable to share AirTag XXX is not eligible for sharing**". I was never asked to type in an Apple ID as described in the documentation. What might be wrong here?