In Fullmetal Alchemist: Brotherhood, the Elric brothers are desperate to atone for their sin of human transmutation and make things right. The Elrics were humbled by their experience, and it gave them some serious perspective as they fought to resist Father's master plan. But their goals and the way they achieved them are completely different from Colonel Roy Mustang's methods.
Roy Mustang is a member of the Amestris military, but he's hardly the brownnosing type. Instead, he has his sights on King Bradley's position, and for years, dreamed of being on top. He is nothing like the villainous Father, but at the same time, Roy's actions and ideals mark him as an antihero to act as a foil, of sorts, to the noble Elric brothers.
Edward and Alphonse go "downward" in their ambitions, since they once arrogantly thought they could use alchemy and science to circumvent the cycle of life and death to bring their mother, Trisha Elric, back to life. Now the humbled brothers seek to maintain the balance of the world, while Roy Mustang goes in the opposite direction. He is a career military man who is determined to climb the ranks, and already, he outranks Major Alex Louis Armstrong as a Colonel, but has his sights set beyond that.
Roy genuinely wants to lead Amestris in a better direction and help the masses, but his methods are pretty close to the border between hero and villain. Unlike the family-oriented Maes Hughes and Major Armstrong, Roy is concerned only about himself and his ability to use others. He doesn't even need to stoop to dirty tricks or blackmail to control people; he can do it through sheer military competence and hard work.
Roy is an antihero because he has the methods of a villain, but the goals of a hero. He considers several fellow officers to be his chess pieces, such as Riza Hawkeye (his best friend) being his queen, the most powerful player. Then there's Lieutenants Falman, Furey and a few others to make a complete chessboard. Roy patiently and methodically moves these "pieces" around to lay down the path for his ascendance as the new ruler of Amestris, and he keeps it quiet, too.
Such subtle and persistent scheming may feel villainous, and indeed, it's a bit cold. When Roy's fellows were scattered across Amestris as part of Bradley's ploy to foil Roy, Roy only thought of it in terms of "oh no, my plan is ruined!" instead of "what if my friends get hurt?" True, Roy trusts his chess pieces to look after themselves, but his first thought was for the sake of his plan, above all else.
Roy Mustang is ruthless and resourceful, and to his enemies, he is downright terrifying, as Lust the assassin and Envy the shapeshifter (both homunculi) can attest to. Roy wields flame alchemy, the unique creation of Riza Hawkeye's father, and Roy mercilessly burns his enemies to cinders, seeking to end a battle ASAP. Roy isn't the type to toy with his enemies or try to reach a peaceful resolution; if a party is designated as a target, Roy will incinerate them without a second thought, acting like a sharpened tool for the Amestris military.
Roy has zero mercy; he cut his transmutation circle onto his skin when Lust injured him, then used his alchemy to cauterize his wounds and then repeatedly blast Lust to death. He later did the same to Envy, and took grim pleasure in vaporizing Envy's eyes and tongue with his pinpoint alchemy, then roasting Envy's entire body with his standard attacks. In fact, when Envy was helpless and cornered, Roy tried to destroy him out of sheer hate and wrath, until Scar, Riza and Edward talked him down.
Roy nearly lost himself to the darkness, a byproduct of his ruthless nature and his attitude that the ends justify the means. But he wasn't entirely a villain in the making; Roy is also motivated to protect the people dearest to him, primarily Maes Hughes and Riza Hawkeye. Roy's rage towards Envy was fueled at least partly by Envy's attempt to harm Riza, and definitely Envy's role in Maes Hughes' death. Roy was disgusted to learn that Envy had triggered the dreadful Ishval Civil War, but the lives of his friends took precedence, especially since the civil war was already over and done.
To Roy's credit, he listened when his friends talked him out of killing Envy, and Envy, inspired by this emotional strength, took his own life and challenged Roy to make the most of this opportunity. Roy did, and he learned humility when he lost his vision to the Gate of Truth and helped his fellows take the fight to Father. Roy had his dark moments, but his bright side shone through, creating a balanced antihero personality.
