I was thinking about the practice of primogeniture this afternoon while taking a walk, and I can really see a lot of practical arguments in favor of it. Passing family wealth (especially real estate) to a single person allows it to concentrate over time; a family that practices primogeniture will grow more powerful over the course of generations, whereas a family that divides its property equally amongst its children will not. In essence, primogeniture creates some of the same benefits that make capitalism sucessful -- except that capitalism facilitates the efficient allocation of resources as well as the concentration of resources. A family that really wants to grow in power should pass its wealth to the most capable child, rather than automatically to the eldest.
Some may argue that such a practice is unfair to younger siblings (or to women, if agnatic primogeniture is practiced), but the heir should always be responsible for the care of his family and should use the family power for the benefit of all its members. Women, of course, will marry into other families, and it wouldn't be fair for them to take a portion of the family wealth with them when they leave.
Historically, especially in England, primogeniture was mandated by law for the inheritance of land. Why? Because it took a large quantity of land to support a knight, and if the land was all split up into tiny parcels there wouldn't be anyone who could afford the training and equipment required.