"Disagreement in fasting does not destroy agreement in the faith." (Solid Declaration)
"...of fasts; although the end of these is to restrain the flesh, reason falsely adds that they are services which justify" (Defense of the AC)
"fasting and other outward preparations serve a good purpose, but... "(Small Catechism)
Jesus begins his instructions on public piety (read regularly at the Ash Wednesday service in the liturgical year) with the words, "When you fast..." He goes on to condemn public displays of fasting, encouraging those who fast to put on an outwardly kempt and cheerful appearance, so that the fast is between you and God.
The Lutheran Confessions say very little about fasting, but what they do say is important, given that fasting makes it into the brief and important Small Catechism and is commented on in two other major texts.
The assumption both in Scripture and in the Lutheran confessional texts is that people are fasting, and will be fasting. This means these texts come out of a different context than ours, a culture that by and large refuses to fast, and even finds the practice unhealthy.
So why do I fast? Not because it does something before God. It accomplishes nothing in the way of justification. But it does restrain the flesh, and God knows my flesh needs restraining. So I fast for the restraint of the flesh. I fast also so that I can understand better the words of Christ, "One does not live by bread alone." These are important words, powerful in our battle against the temptation of the devil. When I fast prior to receiving the Lord's Supper, here fasting indeed serves a good purpose, for then I hunger for Christ, not simply spiritually, but also physically. Christ in His supper becomes a meal for me, and his real presence is real.