Basically God's justice demands not that He punish the wicked but that He punish sinful actions.
So God punished Christ for our sinful actions, thereby allowing Him to forgive us.
It comes from the "Latin view" as it developed from Anselm's satisfaction theory (from Germanic tribal law).
Acquinas developed Substitution focused on merit (the RCC position) and the Reformers altered that view to PSA.
The opposing position is the "classic view" with the overarching theme of Victorious Christ.
Christ suffered at the hands of wicked men, by the predetermined will of God, conquered the grave and freed us from the bondage of sin and death.
God did not cause Christ's suffering, but offered Him as a sin offering (to suffer under the curse that man was under).
God vindicated Christ by raising Him on the third day and glorifying Him.
You have not asked anything.
You said that my belief is influenced by my presuppositions, but have thus far proved unable to identify any presuppositions that I hold.
I know of some (like foundational doctrines must be in "what is written" in God's Word), and I grant I may hold some of which I am unaware.
You just can't seem to identify any.
You have already made that argument.
Ok, I do not disagree with that argument as stated.
At issue are unidentified specifics.
The two deaths of Christ on cross are very important.
The two deaths on the cross are important (although not of equal importance) to Penal Substitution Theory.
But this does not mean that is correct.
It is appointed man once to die and then the Judgment.
The first death is physical.
The second death is when the wicked are cast into the Lake of Fire.
Christ's death paying for our sins was completed before His physical death for His bodily resurrection and our justification in believing in Him. 1 Corinthians 15:17.
So would you put yourself in the Zane Hodges, Bob Wilkin, Tony Evans camp of free grace (or cheap grace as some call it)? One is saved even if there are no signs of rebirth? Jesus said go forth and make disciples, not converts. It follows that when one sees the grievousness of their sins and their need for Christ leading to faith, then they no longer want to live in sin. Preaching the fruit of the Spirit, or works, is not legalism, it is a byproduct of rebirth created by the Holy Spirit. MacArthur simply says that if you are truly born again there will be evidence. The parable of the soils is a good example.
Christ died not pay for our sins.
He became a curse for us, bore our sins bodily, and we are purchased by His blood.
I do not see how the passage you provide supports the idea that Christ died twice (or two deaths).
1 Corinthians 15:16–17
For if the dead are not raised, not even Christ has been raised; and if Christ has not been raised, your faith is worthless; you are still in your sins.
The problem is not the need to exegete what God has said but to accept and understand.
If I say I missed lunch and am hungry you would want me to exegete my hunger.
But the statement stands alone. You would create theories about my hunger, how it relates to spiritual hunger, what it says of the lunch I ate......but I would be simply saying I am hungry.
Those of the flesh cannot understand spiritual things.
I am learning more and more how this is true. What is obvious and plain to many are complicated to others.
The passage means what it says.
God laid our iniquities on Christ, He bore our sins bodily, the Word became flesh, He was made in all things like us, He became a curse for us.
If you need explanations then there is perhaps a deeper underlying issue.
1 Peter 3:18 does not support the false teaching that Christ died a spiritual death. Did he suffer God's wrath due to those who will believe? Yes. The cross contained both spiritual and physical horrors, but at no time did Christ die spiritually.