penal substitution says that God needed an infinite method of having his wrath placated. the only method that is possible, the theory goes, is Jesus dying. his death means you don't have to die as your sins are "covered".
the problem with this idea is that it didn't originate until a thousand years after Jesus and has little basis in the bible. during the early church, the language christians used is called "christus victor". Jesus conquered sin and death on the cross, is the essence of the idea. i like to say love conquers death. anyone belonging to the brotherhood is also saved from death. so, penal substitution isn't orthodox.
what about old testament sacrifices, were they to appease God's wrath? nope. they were a means of saying "i dedicate what i have to you, and turn myself over to you". here is a good quote that shows the true basis for old testament sacrifices and how it ties to Jesus' sacrifice.
"In all of the sacrifices, the central theme is not appeasement, but representational consecration. That is, symbolically through the offering the worshiper says “this offering represents my giving to you my life”, or as you might hear in a love song "God I belong to you, here is my heart". It is not a statement of placation (as if God needed to be bribed into loving us), but an act of devotion, entrusting oneself to God, giving your life into God's hands. In the case of the thanksgiving and first fruits offerings it means that all that we have comes from God and so with these first fruits we acknowledge that it all belongs to God. The passover offering was about the birth of the people of Israel and marked the time of the exodus of God's people out of bondage, so the passover offering was about committing and aligning oneself on God's side against oppression. Finally along with all the other sacrifices the sacrifice of atonement for sin was saying “Here is my life, I want to live it for you Lord. I die to the sinful in me and give my life to you”.
In the same way blood was sprinkled to dedicate the temple, and dedicate the law to God. This was the case with the Passover sacrifice which originated as the people marked their house door showing their allegiance with God, consecrating their house as belonging to the Lord. Thus Jesus when he connects his death with the Passover speaks of a “Covenant” being established by his blood “This cup is the new covenant in my blood, which is poured out for you” (Lk22:20). It was the sealing of a promise, like signing a contract in blood. We can see here that whether a sin offering, or a thanks offering, or a dedication that in every case there is the common theme of consecration – dedicating to God. This sense of consecration is conveyed in the Latin root of the word “sacrifice” which means “to make sacred” or "to consecrate". We give ourselves, our lives, our need, our thanks, our allegiance to God vicariously through the ritual of sacrifice.
There is here the aspect of identification with the animal – you bring a part of yourself to the altar, in many cases laying a hand on the animal's head before it is slaughtered. Specifically in the case of the sacrifice on the Day of Atonement we can see also an aspect of transference as the scapegoat was sent off bearing the sin away (Lv 16:21-22). And as previously mentioned there is here a clear aspect of vicarious atonement specifically with the sin offerings - that animal that died was you. The consecration here meant that the sinner brought their broken life to the altar Yet in all of this the writers of the Old Testament are emphatic that the main object of sacrifice is not about a mechanical transaction detached from relationship, but the outward ritual effecting inner change, devotion, and repentance. As David says
“Cleanse me with hyssop, and I will be clean wash me, and I will be whiter than snow...Create in me a pure heart, O God..." (Ps 51:7,10)
David's prayer here is that the outward cleansing of the hyssop would go down and cleanse his inmost being. God, David says, is not interested in outward actions, but in the state of his heart. This is a relational exchange not a legal one.
"You do not delight in sacrifice, or I would bring it. You do not take pleasure in burnt offerings. The sacrifices of God are a broken spirit. A broken and contrite heart, O God, you will not despise” (Ps 51:16-17)."