Suppose we start with two sexes that have none of the particular attributes of males and females. Call them by their neutral names A and B. All we need specify is that every mating has to be between an A and a B. Now, any animal, whether an A or a B, faces a trade-off. Time and effort devoted to fighting with rivals cannot be spent on rearing existing offspring, and vice versa. Any animal can be expected to balance its effort between these two rival claims. The point I am about to come to is that the As may settle at a different balance from the Bs and that, once they do, there is likely to be an escalating disparity between them.
To see this, suppose that the two sexes, the As and the Bs, differ from one another, right from the start, in whether they can most influence their success by investing in children or by investing in fighting (I’ll use fighting to stand for all kinds of direct competition within one sex). Initially the difference between the sexes can be very slight, since my point will be that there is an inherent tendency for it to grow. Say the As start out with fighting making a greater contribution to their reproductive success than parental behaviour does; the Bs, on the other hand, start out with parental behaviour contributing slightly more than fighting to variation in their reproductive success. This means, for example, that although an A of course benefits from parental care, the difference between a successful carer and an unsuccessful carer among the As is smaller than the difference between a successful fighter and an unsuccessful fighter among the As. Among the Bs, just the reverse is true. So, for a given amount of effort, an A can do itself good by fighting, whereas a B is more likely to do itself good by shifting its effort away from fighting and towards parental care.
In subsequent generations, therefore, the As will fight a bit more than their parents, the Bs will fight a bit less and care a bit more than their parents. Now, the difference between the best A and the worst A with respect to fighting will be even greater, the difference between the best A and the worst A will be even less. Therefore an A has even more to gain by putting its effort into fighting, even less to gain by putting its effort into caring. Exactly the opposite will be true of the Bs as the generations go by. The key idea here is that a small initial difference between the sexes can be self-enhancing: selection can start with an initial, slight difference and make it grow larger and larger, until the As become what we now call males, the Bs what we now call females. The initial difference can be small enough to arise at random. After all, the starting conditions of the two sexes are unlikely to be exactly identical.
From The Selfish Gene. A fantastic explanation of the fundamental difference between the sexes, and why you would expect the asymmetry to arise1. This explains the evolution of the male and female gametes; which in turn explains the disparate strategies adopted by male and female members of a species when it comes to mating.
Evolution is amazing.
1. The only problem with arguments without numbers, such as this one, is I can never be sure if I’m missing a flaw well ensconced in the smooth, convincing wording. I’ve fallen for them too many times!