God is perfectly just. Sin being an afront to God requires that it be punished in keeping with his just nature. Therefore in order to save mankind and be pronounced righteous, satisfaction of God's just nature was required through punishment of all sin. This is where the two theories deviate slightly. Substitution asserts that God transferred the sins of the world to Jesus on the Cross becoming our substitute (in our place) and then poured out divine punishment on him in his death thereby satisfying God's just nature. Satisfaction theory asserts that Jesus remained perfectly righteous, and no sin transferral, but that Jesus took man's punishment on the Cross thereby satisfying God's just nature.
I've come to realize only recently how pervasive either of these theories are among Christians. As I have studied this subject in recent years I've struggled to harmonize either of these views with scripture. I've also found quite a few rather serious doctrinal problems stem from these theories, which we may deal with at some point. As way of intro to some of the harmonization issues I see, Jesus is stated as being pure. How can he be described as these things in Hebrews but as substitution would assert, have our sins transferred to him?
And then with respect to the satisfaction theory, Jesus does not have sin transferred to harmonize with the passage quoted from Hebrews 7, but he's still punished by God. This view then puts God in the position of punishing a PERFECTLY righteous man. (I emphasize perfectly because Jesus is described as without sin, perfect in every way) I then have problems with harmonizing what we know of God revealed in places such as the entire book of Job where he rebukes Eliphaz and his friends for asserting that God punishes righteous men. (Job 42:7) To my best efforts I have not found a scripture that speaks of God dealing out punishment on the righteous. We have scriptures such as the Psalms that speak of how God supports the righteous:Heb 7:26,27 wrote:26 For such a High Priest was fitting for us, who isholy, harmless, undefiled, separate from sinners, and has become higher than the heavens;
27 who does not need daily, as those high priests, to offer up sacrifices, first for His own sins and then for the people’s, for this He did once for all when He offered up Himself.
I see no justice in God punishing a perfectly righteous man, Jesus, as the satisfaction theory would assert. This answer is flawed in that it assumes that God is the one punishing Jesus on the Cross. However, we have scriptures that say that Jesus suffering was at the hand of sinners:Psalms 5:12 wrote:12 For You, O LORD, will bless the righteous;
With favor You will surround him as with a shield.
There is much more I could say but for now let's study together to find what the Word of God would tell us. As a concluding thought I will propose that these theories are asking the wrong question. They ask "Why is God punishing Jesus on the cross?" I find this is laden with assumptions that need to be tested against the Word of God that I'm sure we'll cover.Heb 12:1-3 wrote:1 Therefore we also, since we are surrounded by so great a cloud of witnesses, let us lay aside every weight, and the sin which so easily ensnares us, and let us run with endurance the race that is set before us,
2 looking unto Jesus, the author and finisher of our faith, who for the joy that was set before Him endured the cross, despising the shame, and has sat down at the right hand of the throne of God.
3 For consider Him who endured such hostility from sinners against Himself, lest you become weary and discouraged in your souls.