I am an adoptive parent and I love being one. We often talk about how out family came to be together.
We talk at length about how babies are born and how that happened with a different woman. And we acknowledge that she is also a parent.
If we didn't acknowledge our differences, our DC wouldn't know their birth siblings who we see regularly.
Also, as DH and I both wear glasses, my optician advised we got the children tested when they were quite young for a genetic condition. I wasn't offended or upset. I didn't feel de-parented or not valid when I explained to the optician that we don't have a genetic link. And the optician didn't give a shit either.
I am a parent but I am not a biological parent. And to become a parent was a difficult process, with all kinds of hoops to join and declarations to make.
There was no self identity as a parent, but a rigorous legal process because frankly becoming a parent was fek all to do with us and our rights and feelings, and absolutely everything to do with those of the children, so this analogy not only fails, but it's also a bit insulting actually.