What Discord was a mating abomination between a dragon, pony, griffin, and a lion. He the result that came out.

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I honestly think he's just Chaos incarnate, a Universal Elemental.

Either that, or he got himself cursed.

He's a personification of Chaos, so his physical appearance represents that by being a chaotic mix of various animals. Simple as that.

There IS a fan-theory that's a bit darker though. In that theory, it's said that from the beginning when Discord first came to exist,
he had NO body at all, he was a formless mass of pure chaos-energy given life and thoughts and so on.
SO, in order to create a physical form, he started tricking animals into playing his twisted games,
and if they lost, he took one part from their body and added to his own...
For example, a griffins talon, a dragons tail, two different wings, the paw, a pony's head (which he twisted and morphed into
it's unique look), and the two horns on his head.

And another fan-theory (much less dark) that says he can have any form he wants (as proven by his constant shape/size-shifting),
but he CHOOSES this form because he likes it, it makes him unique and unmistakable.

That multiple-species orgy theory of yours just doesn't make sense. Even if several male animals DID have sex with the same
female, all of different species, the resulting child would NOT be a mix of ALL of them - it would be a mix of the female and ONE
of the males, or more likely, NO child at all due to the species not being genetically compatible.
I mean, I DO see how you think, ut it doesn't add up once you break it down to details and genetics.