The choice of what word to use is a delicate one; one simply does not wish to make a balls-up of it. Thus one may consult a word sommelier:
We have, so far this week, addressed the first four options. Yesterday we looked at the most formal, prim, perhaps even feminine one, effrontery. Today we are at the other end of the scale. I can’t believe he had the balls to do it is not something a politician is likely to say in an interview – you’ll sooner hear it in a sports bar or a garage.
There are, of course, other anatomical references available to express roughly the same concept. Gall is one (a bodily fluid); cheek is another; nerve is a third; guts is slightly different in sense but still in the same general vein. There is even an anatomical reference in effrontery (the forehead). But balls hits below the belt. It is a direct reference to pudenda, and as such is particularly impudent.
Also obviously masculine. Which makes this word undeniably sexist, in that it assigns a certain brashness and nerve to males. This is, of course, a reflection of a general cultural norm; aggressive women have long been described with masculine terms. But at least it’s not a put-down to call a woman ballsy, even if it is an implied put-down of the average member of her sex (let’s see, is there a good way to phrase that without using member and sex? never mind).
Nor is it a put-down of the woman in question to say I can’t believe she had the balls to do it (and it has been said; you can find that very phrase, and others like it, with a simple Google search). Anatomically inaccurate, to be sure, unless the balls in question happen to be some dude’s nuts that she’s squeezing (had having multiple shades of sense available). But aside from the sexism (and, of course, because of cultural sexism), this may be the most admiring of the options. If you use a word like this, it is because you admire courage and confidence and you associate them with masculinity – or at least because you’re willing to make use of a cultural norm that assigns such values.
Now, one might well point out that she had the balls to do it could be a reference to some craft project involving spheres, or perhaps a game of some sort – maybe she just tossed her bat aside and walked to first base. But you know, and I know that you know, and you know that I know that you know, that such reference would have to be specified clearly, and even then the sexual reference would bleed through like pentimento. To give a parallel example, military pilots, referring to flying full throttle, made reference to the dual ball ends on the throttle stick in the phrase balls to the wall, but they clearly did so with a smirk.
Ball, singular, is, true enough, a word that one may use quite innocuously without provoking Beavis-and-Butt-head-type snickerfests. It’s a good old English word with cognates of the same or similar meaning throughout the Germanic languages; it also comes from the same Indo-European root as Latin follis “inflated ball, bellows” and Greek ϕαλλός phallos… yes, that’s right, phallus and balls have the same root. OK, OK… can we continue now?
The point (stop that) is that balls in the plural is by default a reference to balls in the dual, and you know which two balls. The paradoxical association that testicles carry of masculine aggression with vulnerability (and pain!) has led to a few different balls expressions: don’t bust my balls, we’ve got him by the balls, he really made a balls of it, and of course the exclamation Balls!
So, is balls the word you want? If you want to be coarse and admiring and you don’t mind the sexism of it (and you don’t think your audience will mind), then it’s your top choice. It has the same general sonic features as gall, except that it has the /z/ at the end to cap it off; it is a word that is practically made to be bawled loudly. If you want to be even a little proper, however, you’d have to be nuts to use it.