I know the evolutionists try to explain these things in terms of Sexual Selection (Darwin wrote about it) or the need for the creature to identify its own kin and distinguish from others, but still, why the symmetry and the beauty in that case?

Interesting question. Symmetry and beauty are both interesting things to ponder in relation to the creation/evolution question.

Another thought about sexual selection... Sexual selection seems strange to me, for one reason in particular: the "selector" (e.g. a female bird) and the "selectee" (the exceedingly flamboyantly decorated male) are both members of the same genetic population. It makes sense for natural selection to be imposed by the environment (so the population is changing in reaction to the environment), but not to be internally imposed (the population is changing in reaction to... itself?). What good reason is there for females to select ever more colourful males, if colourful males are more prone to being caught by predators? Rather, I'd expect natural selection to favour the females choosing well-camouflaged males that better evade capture by predators. So I don't buy the idea that sexual selection explains brightly-coloured birds such as peacocks.