During His earthly ministry, Jesus was against the Jews who tried to oppose and contradict Him. The Bible tells us, “And Jesus went into the temple, in Solomon’s porch. Then the Jews surrounded Him and said to Him, “How long do You keep us in doubt? If you are the Christ, tell us plainly.” Jesus answered them, I told you and you do not believe. The works that I do in My Father’s name, they bear witness of Me. But you do not believe because you are not of My sheep, as I said to you.” (John 10:24-26). Jesus made it very plain to them that because of their unbelief they were not His sheep. Therefore, Jesus could not be their shepherd.
Jesus went on to tell them about the total security of His sheep. He said, “My sheep hear My voice, and I know them, and they follow Me. And I give them eternal life and they shall never perish; neither shall anyone snatch them out of My hand.” (John 10:27,28). Jesus refers to Himself as “the good Shepherd that gives His life for the sheep.” And again He says, “I am the good Shepherd and know my sheep and I am known by My own.” (John 10:11,14).
Jesus also stated, "Truly, truly, I say to you, 'I am the door of the sheep." (John 10:7). As the good shepherd, He gives His life for the sheep (Verse 11). And being "the door," anyone who enters through that door, "he shall be saved and shall go in and out and find pasture" (verse 9). This tells us about the abundant care and sustenance of the good shepherd of whom David declared, "The Lord is my Shepherd, I shall not want. He makes me lie down in green pastures; He leads me beside the still waters" (Psalm 23:1,2).
The only way one can become a “sheep of Christ,” is in response to the gospel, which is the good news of salvation that Jesus died for our sins, was buried, and rose from the dead in accordance with the scripture (1 Corinthians 15:3,4). Thus, Christ provides “eternal life” for His sheep, which means ”they will never perish; neither shall anyone snatch them out of My hand.”