Many people have seen pairs of Mormon missionaries with their name tags, perhaps bicycling, perhaps walking, occasionally driving a car, men in white shirts and dark trousers or suits, women in "conservative business attire." They are almost ubiquitous, sufficiently familiar to be part of comedic routines (both Mormon and non-) and central to a Broadway play.
Perhaps everyone knows that the eighteen to twenty-four months of mission work for Mormon young people is usually self-financed. Perhaps many know that they are assigned their field of work by LDS Church headquarters some months before they begin. Missionaries have minimal input into their assignments. Having studied Japanese might make it more likely that someone will be called to a Japanese-speaking mission, but it doesn't guarantee that they will. Those making the assignments depend on inspiration and the needs of the Church at the moment. Perhaps a few know that missionaries are assigned to the cities or towns where they work within their particular mission and to the persons they serve with, their "missionary companion," whom they are to address as Elder or Sister so-and-so rather than by their first name. None of those things are a matter of choice. Perhaps even fewer know that missionary companions are to be with one another twenty-four hours a day.
Given 100 or so missionaries in a particular mission area, there is no way of matching them in pairs that guarantees a match of personalities. So every missionary can almost be guaranteed that during his or her time of service one companion will be difficult to live with. Complaining to the mission president that you have a difficult companion is unlikely to help much. However he churns the mix, the result will always be that there are some "mis-matched" missionaries, people who have trouble with one another.
Learning to live with someone very unlike yourself is as much a part of Mormon missionary service as is learning to approach strangers to talk about religion or perhaps learning a foreign language. Sometimes that is the most difficult part of being a missionary. It is difficult to be away from family and friends with no more than weekly contact. Many find it difficult to live a life governed by strict rules: when to arise, when to study, what to study, what to wear, whom to associate with, when to return to one's apartment, what music to listen to, what books to read, when to go to bed. Those serving in countries foreign to them often have difficulty getting used to the food and customs or learning the language. But for months at a time being unable to get away from someone with whom you have a personality difference can be the most difficult thing of all.
It isn't surprising that there are clashes between Mormon missionary companions. What is surprising is that those clashes rarely amount to anything worse than an argument. Most missionaries figure out how to get along with those who are different from themselves. Some learn to be good friends, but more learn to live with another person without demanding that the person, friend or not, be what they desire them to be. They learn that the unity of Christian love is not always a unity of emotional affection. To love someone doesn't require that we share likes and dislikes, habits and practices, or an emotional bond.
Unity is at the heart of the Christian message. Adam and Eve learned in the Garden that not to be one, as we see they are not in Genesis 3:11-13, results in being cut off from the presence of God. But, LDS scripture teaches, their subsequent unity makes it possible once again to have the divine Presence (Moses 5:2-9). Though disunity has far too often marked our relations with one another, Jesus prayed that his followers might have the same unity that he and the Father have (Jn. 17:20-23). The Book of Mormon prophet, Alma, commanded those he baptized "that they should look forward with one eye, having one faith and one baptism, having their hearts knit together in unity and love towards one another" (Mosiah 18:21). The unity of love is fundamental to being a Christian.
Who knows what emotions to ascribe to the Edenic couple, but whether they felt what we think of as love is irrelevant. They were one, together before God, and Jesus' prayer is that we, too, might be one before him. Missionaries learn that they can live in that unity before God with people for whom they do not have affection, that they can love as God loves even those for whom they do not feel the emotion that we call love. Whether missionaries can express the difference reflectively or not, they learn that divine love is deeper than what we ordinarily think of as love, and they learn to have that love for the companions they work with as well as the people they work among.