Why does Faith almost exclusively use the hymns from the hymnal (Lutheran Service Book) during the Divine Service?  There are obviously many other songs--many good songs--written by Christians, and many of them are used in churches.  The first thing to say is that there is no rule or law about this.  It is a matter of what best builds up the congregation "until we all attain to the unity of the faith and of the knowledge of the Son of God, to mature manhood, to the measure of the stature of the fullness of Christ, so that we may no longer be children, tossed to and fro by the waves and carried about by every wind of doctrine" (Ephesians 4:12-14).  

This is the goal of all the public teaching of the Church for the sake of those who have been joined to Christ: unity in the Faith, an increasing knowledge of the Son of God and His work for us, to maturity in Christ.  And all of this is for the purpose that we be increasingly grounded in Christ so that no believer would be moved from that sure foundation.  There are many teachings floating around, and we do not want to be like children in this sense: that we believe everything anyone tells us.  We want to be those who listen only to the voice of our Good Shepherd, Jesus.  

Hymns, like the liturgy and the sermon, are public teaching that we sing to one another.  In other environments, such as in our individual devotions, other songs can and may be beneficial.  But in the worship of the Church as one Body, with one Lord, one Faith, and one Baptism, not everything is beneficial for "corporate" (literally, as the Body) worship.  So, for example, the hymns are very often going to be sung in the plural: "we," "our," "us."  More individualistic songs are not bad, and can be very meaningful, but in our worship together they are not the best.  Especially in a society that is individualistic to the extreme, we all need to be reminded that the Church isn't simply a bunch of individuals collected in one place, but the Body of Christ called together and joined together by the Father, Son, and Holy Spirit.  

This is also why we are very careful about using hymns and songs from other traditions: because the services of the Lord's House shape and form us toward the attaining of full unity in the Faith (the teaching Jesus has given us).  We will never attain that full unity here on earth because sin interferes, but that doesn't mean we give up or despair of unity altogether.  The hymns that teach what we confess and believe from the Scriptures should be front and center, because melodies help us remember words that we might otherwise forget.  Therefore, we do our best to make sure that the words that stick in our brains (because of the music) confess the full counsel of God in the Scriptures concerning Christ.

Here are some other aspects of the Church's song that we consider as we are gathered in the Lord's House as one Body: 

  • A Lutheran hymn is not really about creating the right atmosphere or mood for worship, but it is a vehicle for the Spirit-filled Word of God.

 “The Word of Christ—not the word of man—richly dwells within the Church in psalms, hymns, and spiritual songs. And where the Word of Christ is, there Christ Himself is, doling out His blood-bought gifts. So it is vital not just that a congregation sing hymns which are technically error-free, the hymns must proclaim Christ and His benefits—in a word, the Gospel.” 

  • A Lutheran hymn is not entertainment but proclamation.

The purpose of Evangelical-Lutheran hymnody is not to amuse the crowd or to put on such a grand performance that the congregation jumps to its feet with feverish hand-clapping. The hymns proclaim a divine message which is not entertaining but sustaining, given to feed the sojourning Church as she makes her way through the world, but is not of the world. … The music and song of entertainment aim to gratify the emotions of man but the music and song of the Church aim for something far, far more important: to give voice to the Gospel of salvation which alone satisfies man's deepest need: communion with the incarnate God.” 

  • A Lutheran hymn is shaped by the theology of the cross.

The God who hides and reveals Himself in His crucified Son also hides and reveals Himself in the ways and means whereby this crucified Son comes to us. ...The God who is hidden in the 'foolishness' of the cross is hidden in the 'foolishness' of Baptism's water, the Eucharist's bread and wine, the Absolution's human voice and touch. The offense of the cross now rests within the pulpit, upon the altar, in the font, at the confessional chair. Everything that belongs to God must be crucified, that is, it must hide God so that only those who heed His Word will find Him there, revealing and giving Himself. … Whatever the given subject of the Lutheran hymn—be it the Epiphany, the Church, missions, prayer, or praise—the singer will hear who God really is: the God who reveals Himself and gives Himself to us in His Son. Such hymnody, like the cross itself, will always be a stumbling block to those who seek God apart from where He hides, reveals, and gives Himself. But to those with eyes of faith, eyes enlightened by the Gospel of a crucified Christ, Evangelical-Lutheran hymnody will not be a stumbling block, but an immovable rock of refuge.” 

  • A Lutheran hymn does not only paraphrase Bible verses; instead, it interprets the Scriptures in reference to Christ.

[The] primary purpose of hymnody [is] that it is by nature a preaching-song, a poem that proclaims the Word of God to man, and only secondarily prays to or praises God. … Christ-centered exegesis fathered Christ-centered hymnody. There was no hesitation to preach poetically what was likewise preached in prose. The Word made flesh became the poetic flesh wrapped around the skeleton of any biblical text, whether or not it contained an explicit reference to the Messiah.” 

  • A Lutheran hymn is bound to no culture save the culture of the catholic (universal) Church.

Rather than filling sacred space with 'the kinds of music people listen to all week long,' the Church fills that space with her own music, a melody of beauty and dignity that mirrors her own beauty and dignity as the Bride of Christ. Rather than constantly marrying and divorcing one musical style after another in the ever-changing secular culture, the Church has nurtured her own music in her own culture. Perhaps in days long gone, when Holy Mother Church held great sway over her surrounding culture, her sounds and the world's sounds were not in such disharmony. But today, the sway has vanished. The Church's culture is a counterculture, a culture whose ideals, beliefs, and purposes are at loggerheads with the vast array of secular cultures in which she sojourns. But be not misled: this is not a static and stagnant culture, but vivacious, throbbing with life, for hers is the culture of real, abiding life in the living God. Each generation carefully adds a few fresh strokes to the portrait she has been painting for millennia, but they do not scrap it all to begin anew.”

[The quotaions and the outline are from Chad Bird's book, Why Lutherans Sing What They Sing]