There are many reasons for division. Some are merely historical, though consolidation has largely eliminated ethnically separate Lutheran denominations in the United States. Some are geographic, i.e., the various Lutheran churches may be in fellowship with others, especially in different countries, under other names.
Of course, some is based on doctrine. As I see it, there are basically two doctrinal modes of thinking that creates inter-lutheran denominational differences. One is a view of Scripture: the confessionals say the Bible is the Word of God; therefore, although rules of grammar and context must be observed, they do not separate some parts of Scripture as "man-inspired." The "Liberals" say that the Bible contains God's Word and is a light unto our path, but it also contains human elements: references to the culture of the writers not meant to be universally binding. Thus, liberals are prone to see some injunctions as culturally driven rather than as marking sin, e.g., Paul's writings on the role of women as non-binding, human preference rather than God-given rules.
The other is a question of fellowship. It is difficult to explain in a brief way, but essentially, confessionals are divided by the amount of contact with non-Lutheran influences they are willing to tolerate. It seems to me that the doctrinal break-down among Lutherans exists largely along these two axises.
