I will seek justice
Skybreaker oaths are themed toward justice, fighting for causes, and enforcing social rules. They generally reinforce the importance of moral codes, legal structures, and similar boundaries that protect civilization.
The Skybreakers were the enforcers of the Knights Radiant, often tasked with keeping the peace, policing the other Orders, and making certain that dangerous or dark forces in the world were contained. This sometimes gave them a bad reputation among the more free-thinking Orders of Knights, but the Skybreakers (at their best) were not merciless. They were the ones who believed that nobody, not even a Radiant, should be above being questioned. They were the ones that did the sometimes tough job of making certain that the Orders didn’t abuse their power to become tyrants, as the Skybreakers saw that those with powers could easily oppress those who had none.
They tend to attract those who believe in the importance of legal code, those who have strong moral codes of their own, and those who think the best defense against anarchy are things like patriotism, moral fiber, and rules to govern behavior. Note that the current incarnation, led by the Herald Nale in his madness, is more rigid than the ancient order, which understood that the law was not perfect, but instead represented an ideal to try to reach over time. Anyone believing in finding true justice, in defending the innocent, and in punishing the guilty would be welcome in the Order.