Understanding why Christ had to die
A. Three Necessary Theological Factors
1) Humanity's Sin - All humans have sinned. This is true of us universally (Rom. 3:23). Sin brings guilt and condemnation (Gen. 2:17, Rom. 5:16-18, 6:23, Eph. 2:3). We are totally unable to rid ourselves of our own sin (Gal. 2:16, 2:21).B. Necessity of Maintaining both God's Holiness and Mercy
2) God's Holiness - Unlike us, God is holy. God is righteous, we are not, and therefore, God’s just wrath must come to us. God will not and cannot accept a sinner, because He is holy. The holiness of God results in God necessarily judging sin. Because God is holy, His nature is such that it must judge sin!
(Comment: So far, in points one and two, we do not yet require a cross. God can easily resolve points one and two by punishing our sin. If this were the end of the story, hell would do just fine.)
3) God's Mercy - God, in His mercy, loved us. (Eph. 2:1-4) This is the deciding factor of why there must be a cross. With this third point, God must now devise a means where the standards of His holiness are not compromised, and yet He may justify the ungodly (Rom. 4:5).
1) Absolute Necessity of God's Holiness - God has no choice but to uphold the standards of His holiness, or He would not be God. If He were for one moment let sin go unpunished, He would fail to be the upholder of justice and fail to be God. The necessity of God's holiness is absolute.C. The Cross as the Full Expression of God's Holiness and Mercy
2) Contingent Necessity of God's Mercy - On the other hand, the necessity of God's mercy is not absolute, but contingent. "Jacob I loved, but Esau I hated... I will have mercy on whom I have mercy and I will have compassion on whom I have compassion." (Rom. 9:13-15) Notice, there is no verse like that with holiness! (i.e. "With Dan I've been holy, but with Patrick I've been unholy") Holiness and mercy are not parallel realities in God.
1) Holiness Vindicated - God does not sweep sin under the carpet, but pays for it. Every last bit of our sin is paid by His Son. Think of all the sin of all your life that you have ever committed, every lust, hate, selfishness, pride, disobedience, apathy, greed,... Think of every last drop of sin ever committed, compacted in a moment of judgment, and feel the weight of what you deserve to pay before God.D. Conclusion: The Atonement as God's Self-Satisfaction through Self-Substitution - God substitutes Himself in His Son for His satisfaction. This is the gospel and our hope and the glory of the cross.
Now, compound that with the glorious truth that "(God) made Him who knew no sin to be sin on our behalf." (2 Cor. 5:21) This is staggering. For the holiness of God to be vindicated, every bit of his holy judgment must be borne by His Son, and that is exactly what happened at the cross. The justice of God is satisfied at the cross.
2) Mercy Expressed - The substitution above is the heart of the gospel. Mercy can now be extended to us precisely because the justice of God is satisfied.