Why Jesus said that the God abandoned Him?

God the Father did not forsake or abandon His only begotten Son on that cross. Jesus is quoting Psalm 22 where David was being hunted down by King Saul and he was describing his own feelings of forsakenness.

At vs11-13, "Be not far from me, for trouble is near; For there is none to help. vs12, Many bulls have surrounded me; strong bulls of Bashan have encircled me. Vs13, They open wide their mouth at me, as a raving and roaring lion."

When you read on the following is what David says at verses 23 and 24. "You who fear the Lord, praise Him; All you descendants of Jacob, glorify Him, And stand in awe of Him, all you descendants of Israel.

Vs24, For He has not despised or abhorred the affliction of the afflicted; Neither has He hidden His face from him; But when he cried to Him for help, He heard." I'm sure everyone of us at times felt we were forsaken or abandoned by God due to circumstances that seemed hopeless.

Jesus was not forsaken on that cross either, even though He knew that He would be forsaken by His closest friends. John 16:32, "Behold, an hour is coming, and has already come, for you to be scattered, each to his own home, and to leave Me alone; and yet I am not alone, because the Father is with Me. Also, the Father was in/with Him on that cross reconciling the world to Himself, not counting their trespasses against them, and He has committed to us the word of reconciliation. 2 Corinthians 5:19.

I believe in the Trinity and this is my understanding. Jesus was being expressive so that we can understand what was going on within Him and with the Father on the other side. If He didn't express that, we would not be knowing.

Let's take the case of Abraham sacrificing his son Isaac. God stopped him at the end and provided a ram instead (cf. Gen 22:12-13). Doesn't God knew beforehand that Abraham will obey Him?  Of Course He knew before the foundations of the earth. God withheld Abraham from sacrificing his son but He didn't withheld His own Son (Jesus Christ) for the sake of humans. Therefore now we can say to God what Gen 22:12 says to Abraham — “ For now I know that You love me LORD because You have not withheld Your son, Your only Son for me.”

In Gen 6:6, So the LORD was sorry that He had made mankind on the earth and He was grieved in His heart. Surely God knew the outcome before He made the man, yet He expressed it so that we can understand it grieves God when people sin and destroy themselves thereafter.

When Jesus Christ said “Father, if You are willing, remove this cup from Me; yet not My will, but Yours be done.” - Luke 22:42. Jesus was being expressive about what He was feeling because He is 100% human and He feels all the emotions and pains that we can. Imagine a hypothetical scenario where God has not expressed His feelings in the Bible, we don't understand the heart of God in the first place. Knowingly or unknowingly we know much about God and we can reason and justify the things about God and we can have a relationship with Him because He expressed Himself in the Bible wherever deemed necessary. In the verse Yet not My will, but Yours be done, how many instances have we not used this in church and as well as privately.

The prophecies relating to the suffering of Jesus Christ at the cross were written in Psalm 22 which were fulfilled.My God, My God, why have You forsaken Me?- Matthew 27:46. The Father (who is Holy and sinless) and Jesus Christ (who was carrying quintillions of all human sins at that point in time) cannot be joined together. For what do righteousness and lawlessness share together, or what does light have in common with darkness? - 2 Cor. 6:14. Therefore he was forsaken on our behalf. Whatever Jesus Christ has endured for our sins, we don't have to as a believer, that includes the abandonment / forsaking.

Jesus did not intend by His utterance "My God, My God, why have you forsaken me" to communicate that God had forsaken Him. Indeed, as comments above have pointed out, that would be an heretical reading (to trinitarians).

Rather, He was quoting Psalm 22, which begins with the same phrase. The purpose here was to call this psalm to mind, since it is a Messianic psalm which prophesies the crucifixion. Read further down into this psalm

1 My God, my God, why have you forsaken me? Why are you so far from saving me, so far from the words of my groaning? ... 7 All who see me mock me; they hurl insults, shaking their heads: 8 "He trusts in the LORD; let the LORD rescue him. Let him deliver him, since he delights in him." [Recall the Jews saying of Christ "He saved others, let him save Himself"] ... 10 From birth I was cast upon you; from my mother's womb you have been my God. 11 Do not be far from me, for trouble is near and there is no one to help. 12 Many bulls surround me; strong bulls of Bashan encircle me. 13 Roaring lions tearing their prey open their mouths wide against me. ... 16 Dogs have surrounded me; a band of evil men has encircled me they have pierced my hands and my feet. 17 I can count all my bones; people stare and gloat over me. 18 They divide my garments among them and cast lots for my clothing. [emphases mine]

And, the missionary work to follow the crucifixion and resurrection is also prophesized here

22 I will declare your name to my brothers; in the congregation I will praise you. 23 You who fear the LORD, praise him! All you descendants of Jacob, honor him! Revere him, all you descendants of Israel! 24 For he has not despised or disdained the suffering of the afflicted one; he has not hidden his face from him but has listened to his cry for help. 25 From you [that is, Israel] comes the theme of my praise in the great assembly; before those who fear you will I fulfill my vows. 26 The poor will eat and be satisfied; they who seek the LORD will praise him-- may your hearts live forever! 27 All the ends of the earth will remember and turn to the LORD, and all the families of the nations will bow down before him, 28 for dominion belongs to the LORD and he rules over the nations. 29 All the rich of the earth will feast and worship; all who go down to the dust will kneel before him-- those who cannot keep themselves alive. 30 Posterity will serve him; future generations will be told about the Lord. 31 They will proclaim his righteousness to a people yet unborn-- for he has done it. [emphases again mine]