Yes I find it weird that a sadistic evil cat-man is somehow the dragon born hero of Skyrim in my game , so I get what you're saying

If you want to RP thieves guild and dark brotherhood but don't feel right simply don't touch the main quest. Your character will never have the dragonborn destiny if you don't kill that first dragon

I have completed two of my main objectives in Skyrim at the moment, joined and completed the Dark Brotherhood and the Thieves Guild. I haven't seen a Dragon yet(apart from the one at the start).
I like to be Thief Guild Master and the Listener, I will move onto Mages Guild and Companions next then I will have a look at the main quest, probably will do a lot of misc quests (there are so many!) first though.

Did the same in Oblivion, didn't touch the main quest until many many hours into the game.

Eh, so far I haven't really done the thieve's guild or brotherhood yet, haven't even went to the greybeards and I've over 70 hours played. I came to adventure and kill stuff. I didn't ask to be some silly dragon born. Oh.. you say I'm supposed to do these great things and save the world? That's nice! That's your opinion and if you're happy with it great! My idea is that I'm going to rampage from one side of the continent to the other. If I happen into some happy dragon powers along the way, sweet! They're my powers now you fool and I'll do whatever I feel like doin with'em. I might go along with these guys and rob some folks, clean out some houses, or I might just go along with these shady characters and pillage ever little village, tower, hamlet or town that I come across.

My character's backstory is that he joined the Dark Brotherhood to keep tabs on his brother. His brother and him were called years ago to Skyrim by their father. The boys battled for their family Heirloom and Rashir won. But Aserun the eldest didn't die of his wounds. Instead Aserun joined the Imperials to keep tabs on Rashir. So each brother is in their respective faction because their factions speak. Aserun has settled on eradicating the DB. And Rashir simply only wants to protect himself against Aserun. Rashir took on the job their mother once was in Morrowind, graverobber and petty criminal. And Aserun took after their father's footsteps, respectable job and respectable citizenship. Rashir is the dragonborn. Aserun is not.

Who says you are a hero?

Maybe you are a lucky jerk?

Maybe you got the voice power and said "hey I can use this to kill my enemies".

Just because it's a legend doesn't mean you are a walking stereotype hero who believes it to be anything more then a useful power for getting your way in life.

As for why you'd still kill of all the dragons... well they seem to really dislike and inconvenience you in general and in a personal way.

Don't go to Whiterun until 60 hours in, you should have plenty of time to join the thieves guild and all before you even know you are the dragonborn.