Habakkuk 1:13 ESV “You who are of purer eyes than to see evil and cannot look at wrong, why do you idly look at traitors and remain silent when the wicked swallows up the man more righteous than he?” The point of Habakkuk 1:13, is that the Lord is so Holy that He does not approve evil, yet He has favor on sinners by saving them and if you want to apply this verse to the death of Christ. The question is why did He stay silent when the wicked killed (swallows up) the one more holy then them? That is Christ.
As far as Jesus saying "My God, My God why have you forsaken my" Matthew 27:46 “Now from the sixth hour there was darkness over all the land until the ninth hour. 46And about the ninth hour Jesus cried out with a loud voice, saying, “Eli, Eli, lema sabachthani?” that is, “My God, my God, why have you forsaken me?” 47And some of the bystanders, hearing it, said, “This man is calling Elijah.” 48And one of them at once ran and took a sponge, filled it with sour wine, and put it on a reed and gave it to him to drink. 49But the others said, “Wait, let us see whether Elijah will come to save him.” 50And Jesus cried out again with a loud voice and yielded up his spirit.” Or as Luke recorded it in Luke 23:46 “Then Jesus, calling out with a loud voice, said, “Father, into your hands I commit my spirit!” And having said this he breathed his last.”
But this was not done to fulfill the prophesy of Psalm 22, even those it did, here’s what was done to fulfill Psalm 22:16-18 “For dogs encompass me; a company of evildoers encircles me; they have pierced my hands and feet—17I can count all my bones— they stare and gloat over me; 18they divide my garments among them, and for my clothing they cast lots.
In John 19:33-37 “But when they came to Jesus and saw that he was already dead, they did not break his legs. 34But one of the soldiers pierced his side with a spear, and at once there came out blood and water. 35He who saw it has borne witness—his testimony is true, and he knows that he is telling the truth—that you also may believe. 36For these things took place that the Scripture might be fulfilled: “Not one of his bones will be broken.” 37And again another Scripture says, “They will look on him whom they have pierced.”
And Matthew 27:35 “Then they crucified Him, and divided His garments, casting lots, that it might be fulfilled which was spoken by the prophet: “They divided My garments among them, and for My clothing they cast lots.”
Also Zechariah 12:10 “And I will pour out on the house of David and the inhabitants of Jerusalem a spirit of grace and pleas for mercy, so that, when they look on me, on him whom they have pierced, they shall mourn for him, as one mourns for an only child, and weep bitterly over him, as one weeps over a firstborn.”
These Scripture were fulfilled as was "My God, My God, why have you forsaken my." But Jesus did not say it to fulfill the Scripture, He said it because the wrath of the Father was placed on Him because "He made Him to be sin who knew no sin," Or He was made a sin offering, He suffered the wrath of God for us sinners, we need to look at II Corinthians 5:21 “For our sake he made him to be sin who knew no sin, so that in him we might become the righteousness of God.”
This sounds like Jesus became sin or partakes of sin, we need to look at the context, here's II Corinthians 5:16-21 from the J. B. Phillips Translation. “This means that our knowledge of men can no longer be based on their outward lives (indeed, even though we knew Christ as a man we do not know him like that any longer). For if a man is in Christ he becomes a new person altogether—the past is finished and gone, everything has become fresh and new. All this is God’s doing, for he has reconciled us to himself through Jesus Christ; and he has made us agents of the reconciliation. God was in Christ personally reconciling the world to himself—not counting their sins against them—and has commissioned us with the message of reconciliation. We are now Christ’s ambassadors, as though God were appealing direct to you through us. As his personal representatives we say, “Make your peace with God.” For God caused Christ, who himself knew nothing of sin, actually to be sin for our sakes, so that in Christ we might be made good with the goodness of God.”
The Father did not look away from Christ in the sense that He did not visually look at Him, the Father did place His warth on Christ so that we could be forgiven. When I say we, I am talking about those that the Father has chosen to salvation or those in His definite plan Acts 2:23 “Men of Israel, hear these words: Jesus of Nazareth, a man attested to you by God with mighty works and wonders and signs that God did through him in your midst, as you yourselves know— 23this Jesus, delivered up according to the definite plan and foreknowledge of God, you crucified and killed by the hands of lawless men.”
In that definite plan He chose His people as well, Ephesians 1:3-6 “Blessed be the God and Father of our Lord Jesus Christ, who has blessed us in Christ with every spiritual blessing in the heavenly places, 4even as he chose us in him before the foundation of the world, that we should be holy and blameless before him. In love 5he predestined us for adoption to himself as sons through Jesus Christ, according to the purpose of his will, 6to the praise of his glorious grace, with which he has blessed us in the Beloved.”