Did the Father forsake his Son at the cross?

The quick answer to this question is yes! God the Father did forsake his Son at the cross and I will explain why.

Believe it or not, that was the pre-determined plan of God (Acts 2:23). Also, when Jesus cried out "My God My God why have you forsaken me?", he was fulfilling Psalm 22:1. It is crucial to remember that Jesus was being made an offering for sin by the Father God on purpose. 2 Corinthians 5:21 says, "He who knew no sin was made sin so that we might become the righteousness of God in him (Christ)".  

Mankind's sins state was so hopeless that it required the advent of the perfect sinless Son of God to die ultimately by the hands of God the Father to deliver us from our sins which gave birth to our spiritual death (Eph 2:1; Col 2:13).

The Father punished his Son on the cross and it pleased him to do it (Isa 53:10). Why? Because God so loved the world that he gave his only begotten Son to save the world (John 3:16-17). In order for man to receive everlasting life, Jesus had to die to satisfy the Father's justice and wrath against sin. And since Jesus was made sin by transference, he became the object of the Father's perfect and holy wrath. God who is holy cannot look favorably upon sin because it is evil, and the antithesis of his nature.

That is why Jesus cried out "My God My God, why have you forsaken me?" He was realizing the monumental weight of the burden his Father placed on him - mankind's sins. This was the only time there was a breach in the Father and Son's relationship - at the cross. God had to forsake and turn his back on his Son due to him bearing our sins (Isa 53:5; 1 Peter 2:24). It is also ultimately the reason why he was sent to the earth. 

The human mind can never fully grasp the enormity of this perfect expression of love for undeserving sinners. We must never forget the price it took to purchase our freedom from sin - the precious blood of Jesus Christ. His death was accepted by God so that my life would be secured in him when I repented and believed in his completed work.