God must be immutable, because He said so (Ps 102:25-27). If His plans, attributes, nature, or promises could change then salvation would be impossible, because who's to say He might not change for the bad and become an all powerful wicked tyrant who desires to crush the universe forever? We must have a perpetually good God to trust or else we're lost. But this is a problem, because how will an immutable God save us from sin?
The Scriptures indicate that when Jesus paid the sins of mankind on the cross He became sin (2 Cor 5:21), and a curse (Gal 3:13), at which point His perfect unity with the Father was broken and He cried out "My God, My God, why have you forsaken Me?" (Matt 27:46). The perfect harmony and unity of the Godhead was broken when Jesus confronted sin. If God was immutable when that happened then the eternal fellowship of the trinity would be eternally broken
and He would cease to be God. (This is because His nature is outside of
time, therefore if it is broken at any time it's broken at every time.)
It may be the case that the only thing stronger than sin and death is
God, but it's no less true that it's impossible for an immutable God to pay for our sins. We need to have help from a mutable God.
But that runs into the first problem doesn't it? If our God changes then He can't be counted on to save us, but if He doesn't then we can't get help from Him either. So how can we have an immutable God who is at the same time mutable? Answer: by having Him wrap Himself in humanity and adding our nature to His own. Thus Jesus stepped into manhood and added the ability changing to His unchangingness, so that He would be able to swallow the sins of the world and come out the other side in fellowship with God.
Or in other words, it's only because Jesus lives in time that He can pay for the sins for a time.
In the God-man this difficulty is resolved. The sins don't break His unity with the trinity forever, only temporarily.
One last thought: in Jesus we clearly see mutability wed inseparably to immutability, but how does that work? This is speculation, but I suspect there is a higher, or better name for the attribute that encompass both together without contradiction. For example I was trying to explain a yellow light to the kids and I said "when you see it you either speed up or slow down." They responded, "how can it mean both of those things together?" because they didn't grasp the higher rule, "clear the intersection." I don't know what that attribute or name might be, but I'm convinced that mystery is going to give way to revelation and we'll see it eventually.
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