There are contradictions like this throughout adoption. Birthparents feel it and so do adoptees. Far from being appreciated for what we do on our children's behalf, adoptive parents can actually become the target for our children's anger because we contributed to making them different from the rest of their friends. Neither our story, nor our child's, though, is necessarily public. It's okay to have public versions of private stories.
All adoptive parents have an added dimension to their parenting job.
We need to sort out what's part of a child's normal development, what's part of a child's idiosyncratic behavior, and what's a problem. Sensitized to the emotional issues of adoption, adoptive parents tend to look for psychological meaning behind each of the quirky things our children do. Adopted kids really want to be like everybody else, but they don't always feel that way. They have two families, even if they don't know their birth families. They don't always look like their adoptive families and they don't always feel like they belong.