In the DC Universe, the White Lantern has the ability to control all forms of the emotional color spectrum, and it just so happens that Green Lantern's arch-enemy, Sinestro, is the perfect candidate for those powers.
The White Lanterns first appeared as part of the Blackest Night saga in order to confront the threats of the Black Lanterns. When Nekron floods the galaxy with black power rings, the dead rise from their graves to challenge all life across the universe. Heroes such as Batman and Superman fall to their influence. In order to combat them, a being of white light called Entity is released from the Earth. The opposite of Nekron, Entity is the embodiment of the power that gave birth to life in the universe. It empowers the White Lanterns in order to defeat the threat Nekron poses.
Before they learn of the White Lanterns, a concept that was created by Geoff Johns and Ivan Reis, various leaders of the respective Lantern Corps band together. They know full well it will take the combined might of all their colors in order to defeat the threat. Since they aren’t exactly friends, Sinestro, who is in charge of the color yellow, consistently clashes with Hal Jordan of the Green Lanterns. But Sinestro's complicated backstory inevitably makes him the strongest candidate to become the White Lantern, as well as the first.
Having formerly been a Green Lantern, Sinestro has a connection to that color. But he was also in love with Arin Sur, the sister of Hal Jordan's predecessor Abin Sur. Their relationship allowed Sinestro to feel hope and compassion, and her demise made him feel rage. All of these complicated emotions set Sinestro up as the perfect candidate to become the first White Lantern, whose job it is to embody all of the feelings of the color spectrum at once. He was even foreshadowed to become this force when an image of him of multiple colors was shown in Blackest Night.
Of course, Sinestro's time as the sole White Lantern wasn't meant to last. In order for the Black Lanterns to be defeated, the heroes need an entire Corps to push back the threat. This White Lantern Corps includes Superman, Swamp Thing, the Flash and more. Eventually, Kyle Rayner becomse the universe's sole White Lantern, but the fact remains that a former Green Lantern isn't the strongest choice. Only someone with as tumultuous an emotional history as Sinestro, someone who has touched upon all emotions throughout his life, would be able unlock the full power of the color spectrum and become the ultimate White Lantern.