Why does Jesus say "My God, my God, why have you forsaken me?" This is from the ESV version. It just seems so out of character.
Its a quotation of the first verse of Psalm 22 (Read the whole Psalm), which is a Psalm about a righteous man suffering at the hands of the ungodly, and is traditionally understood within Christianity as being a graphic prophecy of the crucifixion. Hence Jesus would be quoting it to sort of point that out.
Of particular interest is verse 16 (KJV) "For dogs have compassed me: the assembly of the wicked have inclosed me: they pierced my hands and my feet."
Also verse 21, "Save me from the lion's mouth: for thou hast heard me from the horns of the unicorns." Unicorns simply means a one-horned animal, maybe an extinct one-horned rhino, not the mythical unicorn. Anyway, its being used figuratively. Justin Martyr (around 150 AD) in his Dialogue with Trypho, in chapter 91, understood this as symbolizing the cross by the figure of intersecting unicorn horns:
Now, no one could say or prove that the horns of an unicorn represent any other fact or figure than the type which portrays the cross. For the one beam is placed upright, from which the highest extremity is raised up into a horn, when the other beam is fitted on to it, and the ends appear on both sides as horns joined on to the one horn. And the part which is fixed in the centre, on which are suspended those who are crucified, also stands out like a horn; and it also looks like a horn conjoined and fixed with the other horns.
The traditional Christian answer is that at that moment, Jesus took all the sins of everyone who would ever live on himself, and the Father could not look at him in that state. Then for the only time in his existence Jesus was separated from the Father.
Some say that by not looking at Jesus when he took on our sins, the Father thus does not see our sins. If he had looked at him then, God would still see all our sins and we could not be forgiven. This seems to me rather simplistic and taking a metaphor too literally, but maybe there's truth in there.
Sin by definition is separation from God. When The Christ uttered these words, He, Who from all eternity, had known only complete "oneness" with the Father, was completely separated from the Father. The sin of all the world had cast Him into total darkness and "aloneness." Broken (not by The Father, not by The Son... but by sin) was the eternal union.