What does it mean that the Father granted the Son to have life in himself?

Answer:

"Truly, truly, I say to you, he who hears My word, and believes Him who sent Me, has eternal life, and does not come into judgment, but has passed out of death into life. Truly, truly, I say to you, an hour is coming and now is, when the dead will hear the voice of the Son of God, and those who hear will live. For just as the Father has life in Himself, even so He gave to the Son also to have life in Himself; and He gave Him authority to execute judgment, because He is the Son of Man. Do not marvel at this; for an hour is coming, in which all who are in the tombs will hear His voice, and will come forth; those who did the good deeds to a resurrection of life, those who committed the evil deeds to a resurrection of judgment" (John 5:24-29).

In this section of John, Jesus asserts that the Father has granted him rights. He has the right to receive honor (John 5:23), grant eternal life (John 5:24-29), and judge people's lives (John 5:30).

Jesus lays out the criteria for receiving life from him. A person must listen to his teachings and believe that the Father holds everlasting life (Hebrews 11:6). The time has come for the spiritually dead to hear the voice of Jesus and live (Ephesians 2:1; Colossians 2:13). Hearing is not a passive activity, but in the same sense your mother used when she asked, “Did you hear me?” A person who listens to Jesus is someone who does what he asks. The Father has life that is dependent on no one else. He has given life to His creation (Psalms 36:9; Acts 17:25). Jesus has the same power.

• In speaking of Jesus, John said, "All things were made by him; and without him was not any thing made that was made. In him was life; and the life was the light of men" (John 1:3-4).
• "Jesus answered and said to her, 'If you knew the gift of God, and who it is who says to you, 'Give Me a drink,' you would have asked Him, and He would have given you living water'" (John 4:10).
• "Jesus said to him, 'I am the way, and the truth, and the life; no one comes to the Father but through Me'" (John 14:6).

God the Father authorized His Son to give life to whom he deemed worthy. "Jesus spoke these things; and lifting up His eyes to heaven, He said, "Father, the hour has come; glorify Your Son, that the Son may glorify You, even as You gave Him authority over all flesh, that to all whom You have given Him, He may give eternal life. This is eternal life, that they may know You, the only true God, and Jesus Christ whom You have sent" (John 17:1-3).

John 1:4 and John 5:26 are not contradictory. They both indicate the same thing.