Doug Wilson nails the issue,
I want to spend a few moments on why the penal substitution of Christ is the only possible ground of human happiness. My point is not to defend the doctrine here — that has been ably done by others — but rather to show one of the many glorious outworkings of the doctrine. In our life together, whether that life is being lived in family, church, or town, the substitutionary death of Jesus is the only thing that can keep us from becoming scolds who are impossible to live with.
If Jesus was just setting an example, or just doing some other thing external to us, then our imitation of this will tend toward the bossy and censorious. How many moral examples are crushing examples? How many things done for us, outside of us, designed to make us grateful, are actually burdens that are being tied on our backs by Pharisees? But Christ’s example and Christ’s gifts to us are not like that at all. They are true liberation. Why? Because He died in our place, and only because He died in our place.
If we take that away, then morality ceases to be liberation, and becomes what little we learn in lectures full of scolding and hectoring, and finger pointing. It becomes the kind of righteousness that the devil loves to go on about.
Penal Substitution is the only answer because it is the only explanation that adequately deals with the reality of sin. Of course, that’s why many deny penal substitution; because the idea that there is sin that God is angry at is repulsive to them.
When you think about it, denying the reality of sin and God’s judgement is really the homeopathy of atonement. Total wishful thinking that causes us to suffer terribly and never seek the proper cure.