So, I'd totally disgree that Jesus was actually asking why God had forsaken him....because...
"My God, My God, why have you forsaken me..." is just the well known begining of the 22nd Psalm of David, known to the Jews and which Jesus was starting to recite.
So, some of the rest of Psalm 22 that Jesus seemed to be reciting when he died....
To God...
Yet you are enthroned in the holy place O glory of Israel! In you our fathers trusted, and you delivered them. To you they cried and they escaped, in you they trusted, and they were not put to shame.
Yet now I've been made like a worm, not a man, the scorn of men, despised by the people, they scoff at me, and mock me, they say..'He relied on the Lord, let him deliver him, let him rescue him if he loves him'.
**Remember this is a Psalm of David written 1000 years before the time of Jesus**.
But, Father...You have been my guide since I was first formed, my security at my mother's breast, to you I was committed at birth, in my mother's womb you were my God.
Be not far from me now for I am in distress, Be near because I have no one to help me.
Many bullies (strong bulls) encircle me.
My body is like water poured out, all my bones are racked. My heart has become like wax.... My throat is dried up like baked clay....To the dust of death you have brought me down.
Evil doers, a pack of dogs surround me, they have pierced hands and pierced my feet...They look on and gloat.
They divide my clothes and cast lots for them.
Lord be not far from me, hasten to my aid and save my soul.
I proclaim your name to my brethern, in the midst of the assembly I will praise you.
All who respect the Lord praise Him, for he has not spurned nor disdained me, a wretched man in his misery, he does not turn his face from me, but when I cried out, heard me!
So, by this gift I utter praise in the vast assembly. I will fullfill my vows..The lowly shall eat their fill...May your hearts be ever merry...
All the ends of the earth shall now remember and turn to the Lord. All nations shall bow before him. For his dominion is to rule all nations.
To him alone all who sleep in the earth, all the dead shall bow.
And my soul shall live...
Let the coming generations be told, that they may proclaim the Lord to people yet unborn....
So, even though it was written 1000 years before Jesus, it's actually seems to be about a crucified man, and exactly what's happening to Jesus right then, which is why he mentions it, and starts reciting it, so people will know. God just doesn't make him recite the whole thing because it's already been written forever.