After Jesus says, 'I and my Father are one,' his opponents take up stones. When Jesus asks which good work warrants stoning, they answer that the issue is not a good work but blasphemy: 'thou, being a man, makest thyself God.'
John therefore supplies the opponents' own interpretation of the dispute.
Leviticus 24 prescribes severe judgment for blaspheming the divine name, and Jewish monotheism made claims that appeared to compromise God's unique identity extraordinarily serious. The opponents' accusation is evidence of how they understand Jesus' words; an opponent's interpretation does not by itself prove that interpretation correct. In John's narrative, however, Jesus does not answer by saying that they have simply mistaken him for claiming too much.
He proceeds through Scripture to defend his right to call himself the Son of God.
The legal-religious background explains the intensity of the reaction. This is not presented merely as disagreement over an inspiring metaphor.
John has brought the question of Jesus' divine identity explicitly into the narrative: his opponents say that a man is making himself God, and Jesus responds by defending rather than retracting his unique claim.