How does natural selection explain sexual display?
Short answer
Survival does not get your genes into the gene pool, reproduction does.
thus reproduction based selective pressures can be stronger than survival based ones. there are plenty of organisms that die during or right after mating because of this.
Consider an example In species A finding a mate is fairly rare, it may only happen a few times in an organisms life. if individual X is guaranteed to mate and reproduce when they find a mate but will die after mating, and individual Y will not die after mating but only has a low chance to mate then the genes from X will spread much faster than the genes for Y, because mating is already a rare event, but X genes spread every time while Y genes will also only spread once or often not at all, and will also take much longer.
Or to put it another way, a chicken is just an eggs way of making another egg, the survival of the chicken is only useful as much as it facilitates reproduction.
Any mutation  that happens to make you better at attracting a mate will spread, how it does so is basically irrelevant as long as it works, loud noises, bright colors, eye spots anything that draws the females attention works. studies on several bird species have shown even the colored bands used to identify birds for study effect their mating chance is they are right colors. Animals often already have a variety of biases for their attention hijacking them is an easy way to improve your chances of mating.  Of course once a way evolves that reliably improves mating chances preference for that becomes favorable as well which can lead to a run away selection feedback loops AKA Fisherian runaway
https://link.springer.com/article/10.1007/BF00172135