Private confession is available for those who desire it. It's like Resha Caner mentions above, it's not very visible in the Lutheran tradition, but it's there.
It's not about going through a "third party", however. It's about the power and efficacy of God's Means of Grace in Word and Sacrament. When the pastor pronounces forgiveness of sins, either in the public confession of sins or in private confession, he is speaking in persona Christi (in the person of Christ), as Christ Himself is the One who told His apostles, "Whoever's sins you forgive are forgiven them" (John 20:23). This is properly the authority given to the whole Church, but for good order the Church has always called and ordained pastors to be ministers of Word and Sacrament--and as such they are the ones who exercise the Office of the Keys for the good of all the Faithful. And so this treasure of Confession and Absolution is a gift from Christ to us, that we might hear the bold proclamation of the forgiveness of our sins. We might be well to remember our Lord's statement, "So if the Son sets you free, you will be free indeed." (John 8:36).
It is God who mediates His grace through these precious gifts and means of His grace, that we might be fed and nourished by His word, sustained by His Spirit, receive faith, and have life in Christ Jesus our Lord. He does all these things for us, out of His great love toward us. And it is because of His great love toward us, which He showers upon us through such Means, that we can be confident that we belong to Him, for we are God's people, found in Christ, filled with the Spirit, hearing His word, baptized in the name of Father, Son, and Holy Spirit and therefore sealed by the indelible seal of God's grace. Gathered around His Table, confessing our sins, truly forgiven, and sent out into the world as a Christian people with the Gospel on our lips and good works for our neighbor.
-CryptoLutheran