If you have lots of people perform a wide variety of physical tasks, and then look at how performance on one task predicts performance on another, it's not that whoever is good (or bad) at one tends to be good (or bad) at the others, as though there were a single trait like "athleticism" that was being tested in a bunch of different ways.
Rather there are two clusters of traits -- strength (like how hard you can grip something) and coordination (like how long you can balance on one leg). People who are good at one type of strength task tend to be good at the other strength tasks, and those who are good at one type of coordination task tend to be good at the other coordination tasks. However, strength and coordination are not strongly positively related.
We often use "physically fit" or "active" or "athletic" or whatever as a shorthand for some trait that tells us how healthy a potential mate is, whether due to their good genes, good diet, or something else. Yet it's striking how little of a role strength plays in courtship behavior, and instead how much emphasis we place on coordination.
Sure, the guy will often lift the girl off her feet and spin her around, conspicuously carry some heavy stuff, or strike something really hard with his hand or foot (say, hitting the TV or car to make it work). Obviously girls make strength displays even less frequently, aside from sprinting and then leaping into your arms when they spot you from far away, or slamming their hands on a surface to show excitement ("Yes! Yes!").
Far more common are displays of coordination. Girls do all sorts of little but noticeable balancing acts when they're trying to catch a guy's eye -- standing on one leg with their free foot resting on their straightened knee, pushing themselves up on the balls of their feet, standing with their lower legs crossed over each other and their feet close together, spinning around on one leg, bending over to pick something up without bending their knees, and even doing cartwheels.
But even guys do lots of coordination displays, at least the ones who do well in courtship. Not really any of the above things that girls do, but solo dancing, couples dancing, and performing as a musician or actor. The high degree of coordination needed for both types of dancing is obvious. Even the lead singer of a rock band and a captivating actor have to move or jump around in ways that threaten a loss of balance, so that staying on foot and not coming off as a clutz look impressive.
Girls occasionally dream about guys doing feats of strength, like socking someone who deserves it, carrying her in his arms, or opening the applesauce jar. Still, the majority of their fantasies and the displays by real-life males that they pay most attention to involve coordination, mostly musicians and actors, along with some dancers. Employing once again our test of who shows up on the wall of a 15 to 24 year-old girl, i.e. those with highest reproductive value, we see guys who are strong enough to throw a good punch, pick a girl up, and open a jar, but who on the whole cannot make a living by lifting up, transporting, and putting down seriously heavy things all day. Yet they can keep their balance pretty well while throwing their limbs around in complex ways -- Michael J. Fox in Back to the Future, Tom Cruise in the beginning of Risky Business, Michael Hutchence, Mick Jagger, Mario Lopez when he showed off his ballet moves on Saved by the Bell, and so on.
And of course this is not unique to humans -- all of those complicated mating dances that males of other species do involve throwing around their body parts in hard-to-control ways while maintaining their balance (or if they're in flight, while keeping from spinning out of control). Showing the female how heavy of a branch or pebble they can pick up shows up far more rarely.
Girls seem to laugh more at a guy who attempts a daring coordination display and then loses his balance or otherwise comes off as clumsy or a clutz, than a guy who attempts a daring feat of strength but can't pull it off. Male spectators would laugh the other way around, another suggestion that strength is key to male-male competition, while coordination is key to courtship of females.
What's behind this pattern? I think it's symmetry. There is a very extensive literature showing that both sexes in any species are attracted to more symmetrical individuals (not just to their faces, but also to their voices and even the smell of their sweat), that symmetry is a good signal of health, and that symmetry is heritable, meaning that if you mated with a symmetrical person, your children would get a boost in symmetry than if you mated with a less symmetrical person. It's something that is a big deal to us, and to non-human species, even if we're not conscious of it.
How are we supposed to judge another person's symmetry, though? One way is to get a look at them in a still position. Again even though we're not conscious of it, we can tell from a still image if a person is very symmetrical or not. But we don't always have the luxury of looking at a person head-on and while they're still; judging symmetry at any other angle is pretty dicey. If we were close enough, we could smell their scent or hear their voice, since these are more pleasant if the person is more symmetrical. But we can't always get right up next to a person like that.
Coordination displays work as symmetry displays because it's harder for an asymmetrical person to even stand still, let alone throw their limbs and torso and head around. Deviations from symmetry are so minute that they have to be detected with calipers, so I doubt that someone whose right foot is ever so slightly longer than their left foot will be able to sense this (again unconsciously) and to compensate in order to maintain balance while spinning around, etc.
Better yet, coordination displays are visible at a distance and while the judged person is moving, unlike other cues of symmetry. Of course, they work well up-close too, so they're overall better than scent or voice to detect symmetry, and also better than a still image if it's not viewed head-on.
That's why coordination works well to detect symmetry. Why can't strength displays work just as well? Imagine a less symmetrical person lifts a heavy weight, and so does a symmetrical person. The less symmetrical one will probably have a harder time because they have to make special adjustments to stabilize themselves. But this difference will be very hard to detect at any distance -- it's not like the less symmetrical person is going to keel over on their weaker side. If asymmetry between their hands gives them a stronger grip in one hand than the other, that will be hard to spot too.
Not impossible, but hard. And nowhere near as easy as watching an asymmetrical person go for a spin and fall all over themselves, or try to swing their arms to a beat but fail to coordinate them in time with the rhythm and look clumsy. When throwing yourself temporarily off-balance, e.g. by standing on one foot instead of two, you have a lot less room for error because the base area within which your center of gravity can safely go is a lot smaller. So even small imperfections in symmetry can cause a very noticeable mistake in coordination.
One final thought on which trait girls are more worried about. In popular depictions of the last guy in the whole school that a girl would want to go out with, some measure of his repulsiveness is due to his weakness, but much more emphasis is given to what a clutz he is (like Screech or Skippy). Not just hand-eye coordination, like if he can't catch any projectile thrown at him, but a more basic proprioception or kinesthesia. (And of course, equally heavy emphasis is given to how ugly he is, the point of a post a little ways down below.)
And what about what guys themselves worry more about? I've never asked around, but just listening in on their spontaneous remarks about their anxieties, it's rare that you hear a guy get sweaty palms imagining attempting a feat of strength in front of a girl and failing, but extremely common to hear them get worried about how coordinated vs. clumsy they'll look if they try to dance with her or, even worse, solo dance in front of her. Even if there's no one else watching but the one girl. Sure, he'd feel embarrassed if he tried to open a jar but couldn't, but he'd be mortified if he lost his balance or otherwise came off as clumsy, even for a moment.
If the guy is imagining himself in the presence of another guy, clearly it's the opposite: doesn't want to look weak, and isn't so concerned about looking like a clutz. More evidence that strength is for male-male competition, while coordination is for courtship of females, as well as for female courtship of males.