Cross Ange - Tenshi to Ryuu no Rinbu

From MangaHelpers:

All humans in this world can use the power of the light of mana, and those who can't are considered to be subhuman 'Norma.' The world is like a peaceful utopia, and the celebrated princess Angelize leads a happy life. She believes that the only darkness left in the world is the existence of the horrible Norma.

However, in a ceremony on her 16th birthday, the truth is revealed--Princess Angelize is a Norma. Now she is going to learn what her society does to Norma. She is sent to an isolated island full of others like her, who are taught that the only reason they are allowed to live is in order to fight to protect the peace of this world. Now "Ange" is part of a squad that pilots Paramails and fights invading extradimensional dragons.