It is not uncommon when discussing the atonement for someone to bring up the ugly, inappropriate, phrase "the mechanics of the atonement." Generally this is done to protest, either mildly or strongly, against the necessity of knowing the framework of beliefs that sees the atonement as a work of self-giving on the part of the triune God whereby the Son voluntarily agrees to bear the sin of his people by taking their place and bearing their condemnation.
I have never understood that when discussing something so personal as the Father not sparing his own Son but giving him up for us all (Rom. 8:32) or the Son being delivered up for our trespasses, it could ever be thought appropriate to refer to this as the "mechanics of the atonement." The very phrase jars with the profound, personal, God-ward, depths of the meaning of the Cross. In its worst form that phrase is used to obvert attention from this explanation of the atonement (penal substitution) to another. But in doing so, let us be clear, a phrase is being used that creates prejudice and misrepresentation against substitutionary atonement.
It is strangely reassuring to know that Gresham Machen was having to deal with the same prejudice in his own day. Please not how he aims to uncover heart issues in the avoidance of the Bible's teaching about the Cross:
According to Christian belief, Jesus is our Saviour, not by virtue of what he said, not even by virtue of what he was, but by what he did. He is our Saviour, not because he inspired us to live the same kind of life that he lived, but because he took upon himself the dreadful guilt of our sins and bore it instead of us on the cross. Such is the Christian conception of the Cross of Christ. It is ridiculed as being a "subtle theory of the atonement." In reality, it is the plain teaching of the word of God; we know absolutely nothing about an atonement that is not a vicarious atonement, for that is the only atonement of which the New Testament speaks. And this Bible doctrine is not intricate or subtle.
On the contrary, though it involves mysteries, it is itself so simple that a child can understand it. "We deserved eternal death, but the Lord Jesus, because he loved us, died instead of us on the cross"--surely there is nothing very intricate about that. It is not the Bible doctrine of the atonement which is difficult to understand--what are really incomprehensible are the elaborate modern efforts to get rid of the Bible doctrine in the interests of human pride.
Modern liberal preachers do indeed sometimes speak of the "atonement." But they speak of it just as seldom as they possibly can, and one can see plainly that their hearts are elsewhere than at the foot of the Cross. Indeed, at this point, as at many others, one has the feeling that traditional language is being strained to become the expression of totally alien ideas.
J. Gresham Machen, Christianity & Liberalism, p. 118-9