Our sins have separated between us and God. Our sins have not separated God from us. In Him we live and move and have our being, He is closer to the sinner than the sinner's hands and feet. But our sins have an affect on our conscience, and can give us a sense of being unacceptable to God and of being rejected by Him, even if we are sorry for our sins. And our sins cause damage and therefore reap damage. Even if we are forgiven, the ongoing negative consequences from out past sins dog us, and we interpret this as that God is still against me. Our sins also enslave us to the forces of evil, and give them licence to attack and damage us, emotionally, physically and mentally.
There are two ways to deal with our sense of separation from God due to our gulty conscience. One is to confess it and regret it and aim to do better, which God appreciates, but we remain unsure whether we have been remorseful enough of consistent enough to receive forgiveness. Or we can sear our conscience by practising the sin so often that it become normal to us and we feel no guilt over it.
The cross deals with both of these approaches. God reveals to us in the incarnation, life, death and resurrection, that he loves us sufficiently willingly to endure the same sufferings as we have suffered at the hands of men and demons because of our sins. He wants such an intimate relationship with us that He wants to understand what it is like for us to feel abandoned by God and assailed by demons and men. The revelation of the extent to which God will go to connect with us experientially and to allow us to reconnect with Him and observe His character in action, enables us to trust that he is willing to forgive our sins. So we don't have to go on wondering if God has accepted me when I come to Him to make amends.
And the incarnation, life, death and resurrection of Jesus is able to break the hard calloused cauterised heart too. When someone gets a vivid revelation of how mankind treated the perfectly-loving and forgiving One, after they have mocked and spurned the story for so long, but understand that even so Jesus wants their friendship, their heart can be broken and remade whole and soft.
Jesus was not punished for our sins. He experienced the consequences of our sins, as if He were guilty of them. His Father allowed men and demons to unleash their hatred of good upon Him.
This is the sense in which He Himself bore our iniquities; He was forsaken of God. He bore God's wrath, which is being abandoned by Him to the will of men and demons that He had been restraining, but I had nevertheless insisted He not be Lord in my life. When He is not my Lord, He is not My protector, shield, and fortress.