The defining difference between males and females biologically is that males produce smaller gametes than females do. Sperm are much smaller than eggs. This difference is the starting point for most arguments describing how the sexes have evolved divergent traits. In mammal further apparently inescapable differences arise because only females harbor internal development of young, and only females lactate (while male lactation is not unknown, there are no document cases of male lactation providing meaningful nutrition to the young of a species). These three apparently fixed differences underlie most arguments describing the evolution of sexual dimorphisms found in mammals, including the tendency among mammals for females to be the sole caretakers of dependent young.
Paternal care is rarer in mammals than in most other taxa where parental care is the norm. Post-birth maternal care is found in all mammals (most fundamentally in the form of lactation), and females care alone in ~90% of mammal species. This contrasts sharply with birds, where female-only care is found in fewer than ~10% of species. Primates are unusual among mammals in that approximately 40% of genera display at least some male care, according to an older and therefore probably low estimate (Kleiman et al. 1981). Primates provide the opportunity to examine what factors lead to evolution of paternal care, even when sex specific structural factors (internal development and lactation) require maternal care.
Why do so few mammalian males engage in care? Mated individuals face the choice to continue investing in caring of current offspring (bearing fitness costs in the form of time, individual quality and mortality risk), produce new offspring with the same mate, or abandoning mate and young to seek new mating opportunities. In all mammals lack of post-zygotic and post-pregnancy investment from mothers is fatal to the offspring. Males therefore have earlier opportunities to abandon, leaving females to bear these costs for both of them, than females do. Depending upon timing and the particulars of a species' natural history, mothers may also be more likely to successfully raise the young of the abandoning male than a male could be in raising the young of his absent mate.
Males not only have greater opportunity to desert, but also greater potential payoffs. A male's reproductive success increases more rapidly with multiple matings than a female's would (although females may gain social and genetic benefits from multiple matings), and males therefore experience higher variance in reproductive success than females. This variance is often non-random, relying on traits which influence female choice or the outcome of male-male competition. These traits are necessarily expensive in order to serve as honest signals, and potentially reduce males' ability as care-givers (and longevity, reducing their reliability as care givers) as they increase their ability as competitors. Therefore males who have already mated, and therefore have the opportunity to care for their own young, are likely to also be those who could most successfully remate, and have invested heavily in the capacity to do so. A female who has mated may not be of unusually high fitness, and may not gain fitness from remating, particularly given the cost in future grandchildren associated with abandoning current dependent young. Males, lacking internal incubation, are also less certain of parentage of social young (both probabilistically and in terms of lack of individual information) than are females, further reducing the value of social offspring (measured in number of genetic grandchildren). Mated males in this standard case, have more opportunity to desert, lower risk of losing future grandchildren by deserting and higher potential for remating than do mated females. Given these conditions, it is reasonable to turn the question around, and ask not why so few mammalian males care, but why do those mammalian males who care do so?
The clear answer to this question is that these conditions, or at least the fitness inequalities they imply, are not universal. Under certain conditions, males may gain more by continuing to invest in existing offspring than by attempting to produce additional offspring. Where biparental care is necessary for production of successful young, the opportunity cost associated with abandonment and competitive risk taking increases. Under the same condition, male reproductive success is likely to increase less sharply with multiple matings, at least in cases where certainty of paternity is fairly high. If this results in a decrease in non-random variance in male reproductive success, it is likely to also decrease the potential benefit to competing for new matings, and in investing in the weaponry necessary for that competition.
This by the way, was another start to an intro that didn't quite work out. The problem isn't that the analysis is internally flawed, but that it raises issues I don't have the data to address, and doesn't really lead to the question I can answer.