綺麗事{きれいごと} is an expression referring to...well, exactly what its component words suggests, really. It refers to words or ideas that are considered "beautiful" or "proper", generally as contrasted with the more "dirty" and "honest" nature of reality.
If someone is speaking 綺麗事, it generally means they're saying what people want to hear, or what will make them look good, or what adheres to society's ideals - but the implication is that they're not being completely honest, whether it's because they're covering up their real motivations, or refusing to consider a more practical solution that would go against those ideals.
For instance, idealistic superheroes are often accused by more cynical characters of dealing in 綺麗事. If a hero makes a speech about how they would never kill a villain because that would be stooping to their level, someone's likely to respond with そんな綺麗事並べてる場合じゃないんだよ!今あいつを殺さなきゃみんな殺される! ("This isn't the time to be spouting your precious ideals! If we don't kill him now, he'll kill us all!") Similarly, politicians are likely to be accused of dealing in 綺麗事 rather than facing up to real-world issues.
So in the context of the passage you posted, a person dealing in 綺麗事 would be expected to say the "proper" thing - that they're doing this for the sake of saving the world, of giving people hope. But by saying 綺麗事じゃないんだ, the protagonist is rejecting those notions - for him, it's not about all those good and proper things. He's just doing this for selfish reasons - to fulfil his own urges, because the idea of battling the ultimate rival excites him, because he wants to become number one.