The Jews stubbornly insisted that they revealed their ancestry to Abraham by doing as he did. By claiming Abraham as their father at this stage in the discussion they were saying that they were as good as Abraham. [source][source][source]
". . . no principle was more fully established in the popular [1] conviction, than that all Israel had part in the world to come (Sanh. x1), and this, specifically, because of their connection with Abraham. ... Abraham was represented as sitting at the gate of Gehenna, to deliver any Israelite who otherwise might have been consigned to its terrors." [2][source]
Jesus proceeded to repeat the difference between them and Abraham (cf. Galatians 3:16-29). He also implied again that someone other than Abraham was their spiritual father. [source][source][source]