What does John 10:38 mean?

Jesus was cornered by an angry mob of religious leaders, who essentially dared Him to repeat some of his prior claims (John 10:22–24). Jesus did just that, adding that He was "one" with God the Father (John 10:30). This, predictably, led the hostile crowd to attempt to stone Him (John 10:31). In response, Jesus used their own rhetorical tactics against them. He pointed out how God's own Scriptures used the term for "gods" in reference to human beings in some situations (Psalm 82). This left His critics with only two options: claim that the Word of God was in error—a possibility Jesus flatly rejected (John 10:36)—or admit that some such instances are appropriate.

In Jesus' case, He explained how His miraculous works ought to be clear evidence of His truth. This is the same logic used by others when seeing Jesus' divine power (John 3:1–2; 10:19–21). Even if these men do not like what Jesus says, or Jesus personally—even if they do not believe "Him," as an individual—they ought to believe on the basis of these incontrovertible signs. And yet, as expected, they do not want to believe, and so they refuse to accept what Jesus says (John 5:39–40).

Jesus adds more fuel to the fire by making a statement His critics are sure to despise: claiming co-unity with God the Father. That results in another surge in violence, which He is able to mysteriously escape (John 10:39).