In nature, males are typically fancier or more ornate than females.
In nature, most species require both male and female gametes to create a genetic code for their offspring. Male gametes are sperm, female gametes are eggs.
Male sperm fertilises female eggs.
Typically, it is more effort to produce eggs and raise offspring than generate sperm, so, for the most part, males compete for females.
Take peacocks, for instance. The male is clearly the sexy, fancy one - he is brightly coloured, has pretty tail feathers, blah, blah, blah, yawn. The fancier he is, the more likely a female is to let him mate with her; increasing his likelihood of fathering offspring. It's a quantity vs quality strategy for him. So, the male takes great pains to make sure all the females notice him; unfortunately for him, predators do too.
That said, it is the physically weaker, more encumbered sex that has the most to lose from predation. And, no tail (no matter how delightful or large), compares to the difficulty posed to the female by the small army of weakling chicks under her feet.
Frankly, a peahen can't protect her offspring at all. And the peacock point-blank refuses to help her -- his decision was to only follow his other "tail" and then scamper off into the wild once more.
So, what does she do to protect herself and her wee ones?
What's interesting is how often we often forget that, in nature, being plain also serves a deliberate counterbalance to being ornate. Females caregivers in most species are actually evolutionarily designated to be the far plainer sex; in the wild, the more homely she is, the better she is able to hide in plain sight. Her ability to blend into her surroundings is key to the propagation of her genes and the survival of her offspring. She has a quality vs quantity strategy here.
So, for males that plan to invest lower degrees of parental care in their offspring (the more exuberant, sexually promiscuous and dominant the male, typically the lower degrees of parental care), having a female counterpart that acts in a safe and coy manner is not just okay but preferable.
The more varied and advanced the forms of predation, the more sophisticated the means female employs to safeguard herself, her offspring and their physical dwelling (nest).
The reverse is also true -- in species like seahorses, where the male seahorse provides daddy daycare in his specially evolved man pouch (I call it a baby sea horse Bjorn), ornate females compete for his plain self.
For animals who split parenting duties roughly 50:50, the sexes look almost identical. Think emperor penguins. Emperor penguins take turns balancing a tiny, precarious egg between their feet and alternate so the other can go out and feed in the open ocean. Apart from the actual laying of the egg itself, it's a team effort.
As it should be.