At 374e Socrates narrows the scope of his inquiry for suitable guardians for the republic to what nature these candidate guardians ought to have. In a metaphor that he is to employ at least 5 times by my count before Book 6, Socrates says the guardians will be like good guard dogs. His idea is explicit at 376a where he tells us that we are looking for a natural admixture, as in a good dog, that is both gentle and vicious. Gentle towards its owners, those it knows; vicious against strangers, those it does not know. Presumably since it is difficult and even hard to imagine how to educate people into a combination of contrary temperaments, Socrates recommends that these traits are, in our terms, “artificially selected” for, so that they are found by nature in our guardians, in the same way we would breed puppies as guard dogs. This type of selection process, we should note, is a binary: either you have the traits in question or you do not, and selection into the guardian class requires that you do.
Later in Book 5 (454d), when Socrates introduces his radical notion that women are capable of the same achievements as men, albeit at a reduced and inferior level, there seems to be another criterion of selection utilized. Whereas before there was a binary process, into which either one fit or did not, here Socrates acknowledges a spectrum of fitness. In this argument, a woman is not as strong as a man; nevertheless, accommodating her weakness as one of merely degrees, she can do the same things as a guardian man. I will call this type of selection for fitness “scope selection,” over agains the first type, “binary selection.”
However, one can raise the objection that these two standards are at odds with each other. If, in the case of selecting the guardian men in “binary selection,” we were to make accommodations due to nature, as we do in the case of women “scope selection,” then it seems that we could introduce all kinds of cases Socrates wishes to exclude. We could say that a man born with only one arm can do mostly everything a two-armed man can do “provided we acknowledge the reduced workload that only one arm limits him to.” Similar things could be offered in the case of reduced mental capacity or even inferior, flabby bodies. In fact though, at 375c traits such as keen senses, speed and strength are explicitly advocated, showing that Socrates does in fact wish to cultivate a type of guardian, one who is not the best of some particular kind of human (e.g. the best of scrawny men), but a best human in a sense meant to extend to the whole species.
It is unclear then, what prompts Socrates to have two distinct standards, one for male guardians, one for female guardians, when, perhaps ironically, Socrates is in the midst of an argument for the equality, in some sense, of the sexes.