Couple of things going on there.
Off the top of my head:
1. It's not always like that in nature. Consider baboons. It's definitely a tendency, but it's just as definitely not an absolute.
2. Relative male disposability in nature. Those same traits that make, say, a peacock or a male guppy "flashy" to, respectively, peahens and female guppies (and us) also make them easier for predators to catch. The number of peafowl and guppies born each year is governed more by the number of females than the number of males. So, the females tend to be relatively drab, so that they won't get eaten while on the nest/carrying young (guppies are ovoviviparous, meaning they hold their eggs inside until they hatch), but males have to risk being eaten by predators in order to attract the attention of a female. Humans... don't really have that pressure.
3. Patriarchy. Or at least lingering remnants of same. For a good chunk of recent history, middle-class to wealthy men were expected to find jobs (or at least manage their investments or the like). Middle class to wealthy women, on the other hand, were expected to... find husbands. For anyone who wasn't a farmer or similar laborer, men were generally expected to Do Things, while women were... expected to be ornamental, so they could find a man to attach themselves to, and bear and raise his children.
So men's fashion and styles tended to be (relatively) utilitarian, because even "gentlemen" were expected to Do Things (even if they didn't have a job per se, they were expected to do things like hunt, ride, become officers in times of war, and so on), while women's fashion and styles didn't have to be utilitarian as long as they didn't too significantly restrict women from, er, continuing to exist, and once they Found A Man, bearing and raising children.
There are lingering remnants of this in things like high heels, girdles and other restrictive foundation garments, relatively tight or otherwise restrictive women's clothing, and so on.
And probably other factors I'm not thinking of.