Jesus proclaimed how he frees us from our past screw-ups, but some people thought it was phony. In fact, some of them wanted to kill Jesus!
Jesus then talked about how in spite of being a descendant of Abraham, the questioners do not accept Jesus's word and even wanted to kill Jesus (8:37). Jesus also talked about how what they do is impacted by the questioners' "father" (8:38). The questioners thought literally and referred to Abraham, but once again, Jesus had a different view on "father".
Jesus talked about how being a child of Abraham means doing the works of Abraham (8:39). The Greek word for "child" (Strong 5043) does have a literal meaning of "child", but figuratively can have a meaning of "pupil" (which makes sense since Abraham learned from God). In fact, back in Abraham's life (as seen in Genesis and retold in Romans 4), Abraham, while not perfect, trusted and obeyed God. The questioners, however, do not, as evident by desiring to kill the one who relays the message from God. So while the questioners are indeed literal descendants of Abraham, they did not spiritually behave like a child of Abraham.