Stated by those who reject it, the argument runs along four lines, and its proponents are Christian theologians rather than outsiders to the tradition.
The first is about God. Critics argue that the doctrine sets the Father against the Son at the decisive moment, so that the Son protects human beings from the Father, and that whatever the formal safeguards say, this is what is heard from the pulpit and what shapes the piety. The charge that the arrangement amounts to an act of cosmic child abuse was made in those words by a British evangelical writer in the early twenty-first century and set off a dispute inside evangelicalism that has not closed.
The second is about justice. Punishment, on the ordinary understanding of it, is not transferable. Punishing an innocent person instead of a guilty one is the standard example of injustice rather than an instance of it being satisfied, and critics argue that a doctrine which requires the transfer has redefined justice to get the result it wanted. Defenders answer that the case is not ordinary because the substitute is the offended party, which critics in turn hold concedes that the criminal analogy has broken down.
The third is about what the doctrine sanctifies. Feminist, womanist and liberation theologians have argued that a system in which innocent suffering is redemptive supplies a religious justification for enduring abuse, and that this has had measurable pastoral consequences for people advised to bear what was being done to them.
The fourth is historical. Critics hold that penal substitution is a sixteenth century construction dressed as the doctrine of the whole church, that no council defined it, and that the fathers did not teach it. Defenders reply that substitutionary language is patristic even where the penal frame is not systematised.
The atlas holds this argument open. Penal substitution is neither the default from which the other accounts depart nor a late corruption of an earlier purity; both of those are positions that people argue for, and what is recorded here is that they argue.