The Jews who clash with Jesus (John 8) claim to be Abraham’s seed (sperma) and Jesus agrees (v. 37). When the say that Abraham is their father, Jesus demurs: “if you are Abraham’s children (tekna). . . . (v. 39). There’s a difference between being seed of a father and children of a father. What is the difference?
It’s a nature/nurture distinction, but we can be more specific. In John 8, Jesus identifies two characteristics of sons in contrast to seed. If the Jews were truly children of their father Abraham, they would “do the deeds” of their father (v. 39). The father-son relation involves a common pattern of life, as Jesus has already stated concerning His relation with His Father: “the Son can do nothing of Himself, unless something He sees the Father doing” (5:19). The second is a common joy: “Your father Abraham rejoiced to see My day, and he saw it and was glad” (8:56). The Jews want to destroy Jesus instead of rejoicing in Him, and so are not sons.
A good test for fathers to see how they are doing with their kids: Do your children do your deeds? and, Do they share your joys? And behind these questions are others: Should they do your deeds or would they be better off mimicking someone else? Do you rejoice in the truth or something else?