John 8:37

“I know that you are Abraham's seed. Yet you seek to kill me because my word does not have free course in you.”

Jesus then took up their claim to be Abraham's children, and from now on, when He said ‘you', He was certainly referring to the Judaisers as a whole.

‘I know that you are descendants of Abraham.' He did not deny that in the flesh these men could call themselves ‘children of Abraham'. While in many cases it might not be literally true they did belong to a nation whose roots were in Abraham, and they proudly sought to trace their ancestry back to him (even though often the relationship was only by adoption). But He then pointed out that they were not behaving like children of Abraham. ‘Yet you seek to kill me because my words find no place in you'.

Among Israelites ‘son of --' could have two levels of significance. On the one it could indicate ‘by ancestry', on the other it could mean ‘by behaviour'. Thus the ‘sons of Belial' were those who behaved like Belial (Jdg 19:22; 1 Samuel 2:12; 1 Kings 21:10). A true son is revealed by his behaviour. What He was thus saying was that while they might be natural sons of Abraham they did not behave like it and were therefore not true sons of Abraham (compare John the Baptiser's contemptuous dismissal of their claim in Matthew 3:9).

So while there were some among them who were friendly disposed and had given His words entry, the wider group still sought His death, and it was they whom, identifying themselves as ‘children of Abraham', Jesus was addressing.. That Abraham would not have behaved like they did is implied, (and stated in John 8:40), thus they were not truly ‘sons of Abraham'.