Jesus’ fourth saying from the Cross was a question, a question addressed to God (his Father), wherein, he cried with a loud voice saying “My God, my God, why hast thou forsaken me?
Notice, how Jesus, who addressed God as Father, when he asked him to forgive his murderers and who addressed God as Father, when he commended his Spirit into his Father’s hand, is now addressing God as God and not Father, implying that his sonship was severed due to the sin that he had become (2 Corinthians 5:21), for God the Holy Father could have nothing to do with sin, just as light can have no communion with darkness (2 Corinthians 6:14).

The question posed was “Why?”
The answer is “Love” and the object of that Love is “You and me”.

Why did God the Father forsake Jesus?
God so loved the world (you and me) that he forsook his only begotten Son, so that we would not have to cry out “Why have you forsaken me?” Instead, Jesus, the Only begotten Son of God cried out, being God forsaken, so that we who are deserve to be God forsaken because of our sinfulness, can be called the sons and daughters of God.

Points to ponder: 
God’s “Love” for you and me is so great that he demonstrated his love for us, that while we were still sinners, Christ died for us (Romans 5:8), being forsaken by God. Behold, what manner of “Love” the Father has bestowed upon us, that we should be called the sons of God (1 John 3:1) because his very own Son, Jesus Christ, had been forsaken and could not address him as Abba, Father.

Matthew 27:45-47 (KJV)
45 Now from the sixth hour there was darkness over all the land unto the ninth hour.
46 And about the ninth hour Jesus cried with a loud voice, saying, Eli, Eli, lama sabachthani? that is to say, My God, my God, why hast thou forsaken me?
47 Some of them that stood there, when they heard that, said, This man calleth for Elias.