Jesus proclaimed how the questioners were focusing on lies rather than the truth. But rather than accepting Jesus or even trying to learn the evidence to support Jesus, the questioners accuse Jesus even more! They called Jesus a Samaritan who has a demon.
But Jesus did not have a demon; He was focusing on God the entire time (8:49). In fact, Jesus never sought his own glory but focused on honoring the Father (8:50). Jesus also talked about how those who keep Jesus's word means not seeing death (8:51).
The claim, however, raised even more questions! The questioners doubted that Jesus would be any greater than Abraham or the prophets, who physically died. But from the Greek interlinear as well as YLT translation of 8:51, Jesus refers to not experiencing death at the very end, and as seen in John 5, not experiencing death at the end means getting resurrected (which Abraham and the prophets likely experienced or will experience).
Additionally, Jesus talks about how Jesus knows the Father and the Father honors Jesus (8:54-55). Because Jesus has the backing of the Father (as supported by the feats as well as past Scriptures like Isaiah commenting on the person now known as Jesus), his words are important, and it's worth listening to Jesus's words (or even learning about why Jesus is reliable).