Where in the Bible does it say that Jesus died for the sins of humanity? Die he say this? Who made this statement for the first time?
This question is part of the more comprehensive question of the salvific meaning of Jesus death on the cross. At first, we therefore have to talk about Gods will for salvation and then about what it means to speak of Jesus atoning death.
“God’s will for salvation
The New Testament understands Jesus obedient commitment to his Father’s will for us as his answer to Jesus commitment through God, his Father. It was no easy task for the early Church to come to terms with the scandal of a shameful death on the cross of the innocent Jesus of Nazareth. Jesus shameful death on the cross was God’s judgement on the Jewish people, even a curse (c.f. Gal 3:13) and a disgrace for Romans, and as many testimonies confirm, a reason for contempt and ridicule. St Paul writes:
For Jews demand signs and Greeks seek wisdom, but we preach Christ crucified, a stumbling block to Jews and folly to Gentiles (1 Cor 1:22-23).
But the early Church remembered Jesus’ own words at the Last Supper; in the light of Jesus’ Resurrection through God the early Christians became fully aware that on the surface his so scandalous death was caused by the unbelief and the enmity among the people, but that behind it there is God’s will, God’s salvific plan, even God’s love. They recognised in Jesus’ path through suffering and death God’s ‘Must’ (cf. Mk 8:31; Lk 24:7, 26, 44) which is spelled out in some texts of the Old Testament. In one of the chronologically oldest texts of the New Testament, the first letter of St. Paul to the Corinthians, we see that St Paul discovered in his communities after his conversion their conviction in faith that Jesus died for us in accordance with the Scriptures (1 Cor 15:3).
From this arise several approaches to interpret the deeper meaning of Jesus’ death: According to an early interpretation Jesus shares the fate of the prophets who were rejected and killed by Israel (cf. Lk 13:34; Mt 23:29-31:35). Because of this a violent death awaits him in Jerusalem, the city of God, because it is impossible for a prophet to be killed away from Jerusalem (Lk 13:33). The old passion narrative also found in Mark describes Jesus as an innocently suffering just man persecuted by humanity; it sees Jesus’ suffering as being foretold in the lamentation psalm 22. The fourth song of the suffering Servant of God in Isaiah (cf. Isa 52:13-53:12), which was interpreted in the New Testament as a foretelling of the suffering of Jesus and its deeper meaning, gained particular importance. And so Paul can see in Jesus’ death the unfathomable love of God, who does not spare His own son but who gave him for us (cf. Rom 8:32,39; Jn 3:16) to reconcile the world to Himself (cf. 2 Cor 5:18-19). The cross is the external sign of the self-emptying love of God.
Jesus substitutional atoning death
The interpretation of Jesus death as substitutionary suffering and dying can be found in the narratives of the Last Supper in the New Testament. At its core, it therefore goes back to Jesus himself. This can be seen, for example, in the ancient words:
“For the Son of Man came not to be served but to serve, and to give his life a ransom for many” (Mk 10:45).
The interpretation of Jesus’ death as substitutionary suffering can be found in the oldest stories of Christian communities (cf. 1 Cor 15:3) and is repeatedly taken up and deepened in the New Testament (cf. Jn 10:15; 1 Jn 4:10; 1 Pet 2:21-25; 1 Tim 2:6 et all). Paul developed the idea of substitution and even spoke of Jesus dying in our place. He goes as far as to say that Jesus was made for us ‘a curse’ (cf. Gal 3:13), that he, the sinless one, was made for us ‘sin’, so that in him we might become the righteousness of God.” (cf. 2 Cor 5:21) (Katholischer Erwachsenen Katechismus (Catholic Adult-Catechism of the German Bishops Conference), Band 1: Das Glaubensbekenntnis der Kirche, p. 189.
It is thereby important to understand the idea of substitution as found in the Bible as a basic human reality. The thought is based on the insight in the relationship of solidarity of all people. The Bible picks up this thought and turns it into the basic foundation of the whole of the salvation story: Adam acts as representative of all humanity and establishes the solidarity of everyone in sin, Abraham is called to be a blessing for all families (cf. Gen 12:3), Israel the light of all the nations (cf Isa. 42:6). The Bible substantiates this idea with the thought of substitutionary suffering, which can already be found in the 4th Servant Song:
Surely he has borne our infirmities
and carried our diseases...
But he was wounded for our transgressions,
crushed for our iniquities;
upon him was the punishment that made us whole,
and by his bruises we are healed...
yet he bore the sin of many,
and made intercession for the transgressors (Isa 53:4-5:12).
The idea of substitution, which is so central to the Bible, is particularly suited to show how, in faith, Jesus’ death could be our salvation. The consequence of the solidarity of humanity in sin had been the solidarity of all in the fate of dying. This particularly expresses the situation of humanity which is hopeless and without salvation. As Jesus Christ, the fullness of life, shows solidarity with us in death, his death becomes the foundation of a new solidarity. His death becomes the source of new life for all who are under the fate of death (ibid, pp. 188f).