How do you Make a Child Your Own?

In Shelley Burtt's "Lives'" essay in the New York Times Magaine on Feb 15, 2008, she writes, "Your birth children aren't offered to someone else first. As contingent as their existence is on particular circumstances, once they're on their way, there's only one place they can end up. To be confronted, 10 years later, with the physical evidence that my son, this generous soul I loved so deeply, almost belonged to someone else, and almost was someone else, brought tears to my eyes and a knot to my stomach. Ryan was ours not only because we had wanted him but also because another American family had not. How do you make a child your own?"

There are a couple of things that struck me about this passage. First, let me say that I understand what Burtt is getting at. But, I take issue with her first sentence; if you're a birthmother, your birth children ARE offered to someone else first. Second, I think it's strange that after living with her son for almost a decade, she suddenly realizes that he had "almost belonged to someone else, and almost was someone else." She adopted him. Did she completely disregard the fact that he had birthparents and a point of origin before she came along? Why does it bring "tears to [her] eyes and a knot to [her] stomach" only that another American family had not adopted adopted him, not that he was taken away from his original family?