This might be an unpopular answer, but it makes all the difference in the world. I want my family line to continue; I want my parents and grandparents to see physical features and behavior quirks in their (great-)grandchild that I haven't even noticed.
It's a primal urge and I can't explain it rationally except to say that I'm human and no exception to what we are hard-wired for.
This brand of rationality is very alien to me. It makes all the difference in the world if the child is genetically one's own child. It is not a toy or a cat. It is an emotional extension of your own being that culminates in having its own identity. It is both you and not you. I fear that if you cannot intuitively grok the difference that it makes, there is no 'rational' way to convince you that it matters.