What does John 10:29 mean?
When explaining His ministry using shepherding analogies (John 10:1–14), Jesus made the claim that His authority was given by God the Father (John 10:17–18). This caused controversy and debate. Some thought Jesus was insane (John 10:20). Others believed His miracles proved He was a sincere messenger of God (John 10:21). The men accosting Jesus now are entirely convinced He's wrong. They have cornered Jesus in an awkward location in the temple (John 10:23), probably already armed with rocks (John 10:31), and are daring Him to repeat these claims (John 10:24).In response, Jesus pointed out that their disbelief was the result of stubbornness (John 5:39–40). They were not willing to believe since they were not part of the "sheep" given to Jesus by the Father (John 10:25–27). Jesus then continued to proclaim that the eternal life He offers (John 3:16) is absolutely irrevocable. In the prior verse, Jesus uses a Greek phrasing that is emphatic and forceful: they will not perish for all of eternity.
Here, Jesus again links His power and authority with that of God the Father. Those who are saved through Jesus Christ are saved because they are "given" to Jesus by God. Jesus once again uses the symbolism of being "snatched," which He referred to in the prior verse (John 10:28) as well as His earlier statements about eternal life (John 10:12). Here, though, He indicates that it is the hand of the Father from which they cannot be taken.
The implication is that the hand of Jesus—the actions and intent—is identical to the hand of the Father: a conclusion Jesus is about to state very directly.