Ok I got some vibes or general feelings from some sentences [@VerusEbuyllio].

'We are the ones that they wanted' and 'special powers started appearing around the world 200 years ago.'

^ This made me think that our main characters are being searched for or hunted.  
and the two hundred years point made me think that its an old tradition to do this hunting of the 'special ones'.

so putting ^ that together and I thought possibly we might have some demons/non-human freakish things with special powers out there.

and that there might be a league of demon hunters who according to our story teller here ^ are evil.  

But these freakish special things are outcasts through seemingly no fault of their own and they are being hunted by things that they are so afraid of that they can't even bring themselves to mention their name.  'we are the ones that "[u]they wanted"'[/u]

who are they:?  
some aliens?
a more powerful race?
just humans more advanced in technology that they can scare special ones witless?
Or 


It just might seem that the they are scientists with a lot of money and advanced field research.
Because of these lines, "but still only 5% are able to develop any type of quirk."

(I know I kind of twisted your sentence there and it was meant to be from the special ones perspective, but I thought a researcher in the field might know that, if scientists are a possibility in this story. ^)


but then there's these other lines where, "some say its radiation, others are convinced the government put chemicals into our water and food to activate this gene, but the truth is we don't know what causes it."

This sounds like the words of a lab rat writing into their journal and hoping their master doesn't see that his lab rat misbehaved.  

how would these specials ones react to getting captured I wonder? would they be angry? scared? afraid? happy to have their constant struggle for freedom come to an end permanently?

also it would be interesting to know that if there was a different mutation between different special ones, would it be negative or positive.  
(for example: a missing limb or changing skin color could be a negative mutation or a positive mutation respectively.)

But the last few lines about the World Experimental Source Tower is interesting.  

"The truth is that they are taking us, no matter the age, and forcing these Quirks out of us via tests. But we will get free, we will see beyond the horizon."

^ Are they afraid of the special ones quirks/powers that they have to remove them?  Why would they be afraid?  Would it be that some quirks are dangerous?  (some knowledge gathering related quirk, or a flame quirk, come to mind as possible dangers to the WEST towers plans.  

Or is it purely a persecution standpoint that the special ones did something back in history to piss off their captors.  And the Captors grudge has lasted generations if not centuries?

And so the Captors return the favor by assimilating the special ones back in society as common ones.  Regular, lame, boring, pathetic individuals that no one could ever like as a friend.  Instead of thinking of these common ones as friends it would be like they are invisible the worst kind of suffering, isolation.