I'm not sure I'm qualified to explain why private confession and absolution has come into disuse in the Lutheran church. Below I've copied a portion of the rule of the Society of the Holy Trinity that lays out some practical pastoral guidelines re: how to re-establish private confession in our churches. They are as good as any I know. A short list of why private confession has gone into disuse would include at least these:
1. The triumph of the therapeutic. We don't got before the pastor to confess sin but to work through issues. Thus we tend not to go to pastors anymore but rather to therapists. This is not all bad. Therapy is incredibly helpful for millions of people. But in our context the rise of therapy and the decline of individual confession go hand in hand. The fact that therapists in the context of their work cannot or do not offer the absolution is more problematic.
2. Meaning-making rather than repentance. It is often claimed that our is a culture that is asking, "How can I make sense out of life?", not, as before, "How can I get out of the hands of any angry God?" I don't know about this one.
3. Individual confession was divorced from the preparatory rites of people who would be receiving the sacrament of Holy Communion. Weekly reception of the Lord's Supper meant the impracticability of hearing confession of all penitents each week.
4. We just don't believe sin is that big of a deal anymore.
5. We don't believe that the pastor in his/her office truly speaks as if from God Himself.
These are the major reasons, I imagine. I'm sure there are more. Not that private confession has gone into disuse, it is hard to imagine how congregations would introduce it again. We need more pastors and theologians thinking through these things. The Society of the Holy Trinity is a good place to start.
CONFESSION AND ABSOLUTION
Individual or personal confession of sins is to be kept and used by us for the sake of the absolution, which is the word of forgiveness spoken by a fellow pastor as from God himself. Therefore, members will:
Learn and adopt the understanding and practice of Confession and Absolution as described in the Augsburg Confession (Article XI, XII, XXV), and the Small Catechism.
Seek out a trustworthy pastor who will be willing to serve as a confessor and who will be able to be available for one's individual confession regularly and frequently.
Prepare to make individual confession by examining one's personal life and relationship with God and others in the light of the Ten Commandments. Also helpful are the penitential Psalms (6, 32, 38, 51, 102, 130, 143) and the Prayer of Manasseh in the Apocrypha.
In preparation for hearing the confession of others, make regular and frequent use of Confession and Absolution, keep confidences, so as to be worthy of the trust of others, read and reflect on the Holy Scriptures so as to provide a reservoir of passages with which to comfort consciences and strengthen the faith of penitents (see FC, SD XI.28-32).
Both as penitent and confessor, refrain from extraneous conversation so that attention is centered on the penitent's confession of sins, the Absolution or forgiveness of sins, and the confessor's use of Scripture passages which comfort the conscience and encourage faith in the Word of God which absolves; refrain from challenging or evaluating the confession; use the order of Confession and Absolution of the Small Catechism or that of the service books of the Church.
As absolved penitents, expect to be held accountable by the confessor for reconciliation with those whom we have offended and restoration of what we have taken or broken.
Confession and Absolution is a sacramental rite of the Church (AP XII.4) and therefore is normally conducted in church buildings where provision can be made for privacy and confidentiality.
Since Confession and Absolution has fallen into disuse among many of us, its restoration demands utmost care and concern for both penitent and confessor. Introduction to and initial use of Confession and Absolution may call for simply following the order of Confession and Absolution lest the penitent worry about a full enumeration of sins or the confessor about comforting and encouraging with passages of Scripture.