If someone is forced to take the punishment for sin (Jesus), doesn't that mean that God never forgives? Even if Jesus is God Himself and He took the punishment Himself, that would still mean that He never forgives, because He would rather punish Himself than show forgiveness for sin, right?
Not only is God loving, merciful and forgiving, He is also just. God will not allow sinful deeds to go unpunished:


He loves righteousness and justice; the earth is full of the steadfast love of the Lord. (Psalms 33:5)
Righteousness and justice are the foundation of your throne;
steadfast love and faithfulness go before you. (Psalms 89:4)
I said in my heart, God will judge the righteous and the wicked, for there is a time for every matter and for every work. (Ecclesiastes 3:17)
For the wrath of God is revealed from heaven against all ungodliness and unrighteousness of men, who by their unrighteousness suppress the truth. (Romans 1:18)
Beloved, never avenge yourselves, but leave it to the wrath of God, for it is written, &quot;Vengeance is mine, I will repay, says the Lord.&quot; (Romans 12:19)
For he is God's servant for your good. But if you do wrong, be afraid, for he does not bear the sword in vain. For he is the servant of God, an avenger who carries out God's wrath on the wrongdoer. (Romans 13:4)
For the wrath of God is revealed from heaven against all ungodliness and unrighteousness of men, who by their unrighteousness suppress the truth. (Colossians 3:35)


At the same time, God is loving, and as such He does not want us to suffer. In keeping with His loving and just nature, God chose to willing take on human flesh and take the punishment that we all deserve:


Say to them, As I live, declares the Lord GOD, I have no pleasure in the death of the wicked, but that the wicked turn from his way and live; turn back, turn back from your evil ways, for why will you die, O house of Israel? (Ezekiel 33:11)
For God so loved the world, that he gave his only Son, that whoever believes in him should not perish but have eternal life. (John 3:16)
He made the one who did not know sin to be sin for us, so that in him we might become the righteousness of God. (2 Corinthians 5:21)
And you, who were dead in your trespasses and the uncircumcision of your flesh, God made alive together with him, having forgiven us all our trespasses, by canceling the record of debt that stood against us with its legal demands. This he set aside, nailing it to the cross. (Colossians 2:13-14)
The Lord is not slow to fulfill his promise as some count slowness, but is patient toward you, not wishing that any should perish, but that all should reach repentance. (2 Peter 3:9)


Because Jesus is God, who is eternal, and lived a sinless life, He is capable of justly paying the price for our sins in our place. Additionally, His sacrifice parallels Adam's original sin; where as Adam's trespass led to condemnation for all men, so Jesus's one act of righteousness leads to justification and life for all men:

Therefore, just as sin came into the world through one man, and death through sin, and so death spread to all men because all sinned— for sin indeed was in the world before the law was given, but sin is not counted where there is no law. Yet death reigned from Adam to Moses, even over those whose sinning was not like the transgression of Adam, who was a type of the one who was to come.
But the free gift is not like the trespass. For if many died through one man’s trespass, much more have the grace of God and the free gift by the grace of that one man Jesus Christ abounded for many. And the free gift is not like the result of that one man’s sin. For the judgment following one trespass brought condemnation, but the free gift following many trespasses brought justification. For if, because of one man’s trespass, death reigned through that one man, much more will those who receive the abundance of grace and the free gift of righteousness reign in life through the one man Jesus Christ.
Therefore, as one trespass led to condemnation for all men, so one act of righteousness leads to justification and life for all men. For as by the one man’s disobedience the many were made sinners, so by the one man’s obedience the many will be made righteous. Now the law came in to increase the trespass, but where sin increased, grace abounded all the more, so that, as sin reigned in death, grace also might reign through righteousness leading to eternal life through Jesus Christ our Lord. (Romans 5:12-21)