@tigrrrlily, I'm sure that many people do introduce it this way. That is certainly effective and polite.
this is also a question about identity. Human like labels. We have man, woman, gay, Asian, teenager, teacher, American, bad, artist, etc... We tend to get upset when things defy or don't have labels. We also use them to define ourselves. The problem with secondary is that sometimes it is not only a descriptor but it can come to be a part of our identity. Like the whole thing with an introduction. I'm not ok being labeled something that I wouldn't be ok being introduced by. That's the problem with secondary. As a descriptor it may occasionally be accurate but as an identity, it's shitty. Many of us do form important parts of our identity around our relationships. It's difficult not to. In that sense, its difficult for me to accept secondary.