The major civilizations of Eurasia found different ways to integrate (a) systems of kinship and descent, with roots stretching back into the deep history of Neolithic demic expansions, (b) states and state formation, along meta-ethnic frontiers and elsewhere, and (c) major world religions. In the case of the Islamic world, something about (a) kinship, marriage, and descent is reflected in this map, which shows percentages of consanguineal marriages (first and second cousins) around the world today.
Southern India has a tradition where men from group A take wives from group B and vice versa, which can result after a generation in cousin marriage. The Islamic Middle East and Central Asia, a culture area formed in the course of the great Arab conquests of the seventh and eighth centuries, have another kind of cousin marriage, where marriages are kept within a patriline: i.e. it is common for a man to marry his father’s brother’s daughter. Such marriages are not directly encouraged by Muslim law. However Muslim rules of inheritance may indirectly encourage them. Under traditional Muslim law, each daughter gets one share of inheritance; each son gets two shares. This is a better deal for women than the one where sons get everything (as in traditional China, for example). But it means that a lineage can expect to lose a third of its property with each generation if it lets daughters marry out.
There is probably more going on, though, than just inheritance law: marriage within the patrilineage long predates the rise of Islam among Near Eastern pastoralists. It is probably connected with another characteristic of this culture area: an intense culture of honor, including a high premium on female purity (guaranteeing the integrity of the patrilineage). To allow a daughter or sister to be seduced by an outsider is deeply dishonorable. But even a legitimate marriage to an outsider carries some shame, putting the wife-giving family in an inferior relation to the wife-takers. Not letting daughters and sisters marry outside the patriline is one way for a lineage to advertise its honor. One of the classic studies of the culture of honor in the Mediterranean is entitled The Fate of Shechem; the story of Shechem and Dinah and her brothers (Genesis 34) exemplifies the valuation of honor over alliance.
There is another characteristic of the Islamic world that may also relate to the culture of honor. Mohammed is unique in being the founder both of (b) an empire and of (c) a major world religion. This is probably not just historical happenstance. A secular conqueror like Alexander or Attila would have had a hard time getting his career going in the Arabian peninsula, because the culture of honor makes it difficult for one man to take orders from another. Treating cooperation as submission to God, rather than to another man, is a way around this problem.