Before you even get started, if you don't like reading long texts, there is a TL;DR at the bottom. You're welcome.
I have played Skyrim a lot.
I have put hundreds, if not thousands, of hours into the 360 version of the game and loved every moment. I now have a decent laptop capable of running this and most games on medium-high graphics and now appreciate Skyrim more than ever before, already putting in over a hundred hours. (thank you, mods)
But, something has not changed throughout any platform, or even any of my playthroughs of the game - I cannot stand to be a 'beast' race, i.e Khajit or Argonian.
I'm not 'racist', in that I really enjoy both of their lores and having them populate the world, as a matter of fact Kharjo is one of my favorite vanilla followers and I've always liked the nice Argonian lady at the Windhelm docks, but just the thought of playing as one of them makes me cringe.
In my ever-humble opinion, I feel as if the Dragonborn should not - cannot - be either of the two. It just doesn't make sense to me. The Dragonborn is an all-powerful, dragon-slaying, prophecy-fulfilling sonuva[censored], not some slimy lizard of flea-ridden cat. It should be some burly Human, utilizing his physical strength to dominate any and all before him; it should be a brilliant Elf, using the powers of lightning, fire, and frost, or any magic, to destroy his opponents. This can be vise-versa and rearranged with any combination, such as an Altmer warrior and a Nord wizard, but just the concept of having a furry cat being the hero of the world doesn't sit well with me.
Don't me get wrong, I like Khajit and Argonians, but I just cannot view them as being the Dragonborn.
I guess I'm coming off as kind of an ass, but this is just my opinion, and if nothing else, I feel as if playing as either Khajit or Argonian is awkward and feels as if the majority of the population of Skyrim dislikes me, even before I kill them. Trust me, bandits, I know Skyrim is for the Nords, I don't want to be here, either.
TL;DR: In my opinion, Argonians and Khajits should not Dragonborn. A cat or a lizard should not be the hero of the world. I know people will disagree and I'm curious to see their opinions on this. That being said, I know people can play as whatever character they wish and make them whoever they want to be. This is all just my opinion.