The Principle of Equality is attributed to Rawls (Gosepath) and suggests that the starting point when determining how best to distribute wealth in society is to assume that it should be distributed equally. This does not mean that it has no other applications; it does, but Rawls was most concerned with how to design the fairest society. In order to show why the principle of equality is justified, I need to deal with it in its broader form; that is, in a form not concerned only with distributional justice.
The principle of equality suggests that the starting point is that any differences that we observe are not morally significant, unless it can be shown that they are. To illustrate what this means and why it is a good idea, I will examine the principle as applied to biases of colonizers, who used differences between them and the colonized people to justify slavery and mistreatment. A powerful group that encounters a less-powerful group that is different in some way (for instance, has a different language, different social norms, or different religion) will naturally assume that the other group is inferior, and will often say that the other group is not merely materially weaker but actually morally inferior. So, for instance, because the Native Americans did not have written language and were not Christian, they were considered to be morally inferior to the European colonizers, and the European colonizers held that this warranted displacing the natives to exploit the New World’s riches for themselves.
There are two consequences of this: an epistemic consequence and a practical one. Epistemically, assuming that a difference is morally significant has led to some very bad decisions. One such decision was named above; another such decision would be assigning women a lesser role politically and personally. Once such a decision is made, it is challenging for the group treated differently to establish that it is worthy of equal treatment, because if the starting point is inequality, establishing equality means that an individual needs to account not just for his own behavior but also for the behavior of all of his fellows.
So, for instance, Sequoyah — who developed the Native American writing system — could not prove to Europeans that Natives were their moral equal, because they could simply point to all of the Native Americans who were less well-educated than Sequoyah. But if the starting point is equality, then it is much easier to prove an inequality, where it exists. For instance, if the starting point is that men are the equal of all animals, then from the generally-accepted principle that it is better to be able to think about morality than to not be able to, it is easy to show that animals are not capable of thinking about morality and therefore than man occupies a special position relative to them.
There is also a practical consequence, as I mentioned before. If the starting principle is that an unequal distribution is presumptively unfair, then those in power have the ability to prevent or ignore a shift towards a more equal distribution. They could, for instance, suppress evidence that the distribution is unfair, or they could simply ignore it. But if the starting point is an equal society, then no such imbalance exists. If any deviation from the position of equality needs to be justified, then it is much harder for those who would make society unequal in their favor to do so, compared to a situation in which all they need to do is conceal the evidence that the existing distribution is unfair. Therefore, for practical and epistemological reasons, the principle of equality is justified.