Equality has no unified meaning, so as an idea it is understood as a social justice issue not as a principle. In this case equality is a revolt against nature, as it goes against property rights. Property rights are inherit or natural and imply inequality.
No, sorry. That's not true. That's metaphysics. Rights as inherent is metaphysics. It has no connection with physical reality beyond the indirect mechanism that is that creatures believe in it.
Regarding main topic
Note: I will use the terms ethical and moral not only in the sense of behavior, but also in the broader sense of what is ethical and moral to think and feel.
Well, as you (TA) know, and the replies in this thread indicate... there is no answer to this in an objective sense because the question assumes that people are equal. A very clever socratic way to illustrate that people are in fact not equal in any real sense (even when it comes to "rights", how things "should" be, etc). Claiming that people aren't equal would just result in you being flamed massively with much pee all over the thread.
Humans have a tendency to try to internally make objective their preferences for general human behavior, feelings towards each other and thoughts about each other, and as such incorporate this preference into the rest of their perception of reality. Once people interact and a mediated objective reality of ethics and morality manifests itself and is continually developed, one has this phenomena in a societal semi-hivemind scale.
Results from this are the ideas and systems that fall under the categories Ethics and Morality.
While of course, entirely delusional, this can have a function for groups, as people liable to see norms of social behavior and the moral/ethical concepts they are implications of as the true ideal. The objective ideal. As an inherent part of the universe, as something beyond preference. As... what things "should" be like. Objectively "should". Not "should if we are to [insert pragmatic reason] but really truly just "should".
On a cultural scale, this results in people treating aspects of societal or sub-societal preference for how people should behave as
knowledge of how people should behave, and this increases resistance in most individuals both towards social deviancy from others, and towards social deviancy from themselves. It functions here as providing a high degree of social stability. It even influences people go against and suppress their own subjective preference because they have learned what the true "should" is from others.
Some of you may have noticed how some fringe religious individuals think atheists could just go murder or rape someone or whatever and be fine with it if it wasn't for legal(retribution) consequence. This is because the religious individual can have its theology as the provider of the axioms that justify their particular set of ethics and morality. They can regard individuals who does not have any such metaphysical belief as the basis for objective morality as simply not being able to have a system of ethics or morals at all, because there is no foundation for it in the science adhering atheist when it comes to its idea of how the universe works.
But... as we have seen throughout history and see every day and know from personal experience, even without a proposed physical/reality basis for an ethical or moral system being objective in some sense, people still go around shoving their preferences into ethical/moral frameworks and even argue about them with each other at length. Often metaphysical concepts are created to serve as basis for ethical or moral belief systems. Seen as evident or implicative of things that don't really necessitate them at all, nor support them as existing.
Property as inherent in reality is one of them. Equality as inherent is another. Heritage and divine right were quite popular in their days. In some ways it still is within capitalist morality relying on the idea of property rights (we do not treat society and as a part of that, economically directive positions in government of nations as hereditary anymore, but we still allow someone to inherit massive economy directive power through full property inheritance). Rights is a metalevel up from some of those just mentioned and is one as well.
They all serve to make objective the societal and individual preferences of humans, though they themselves are not a part of reality in any other way than through our actions and beliefs.
There are other ways than attempting to make human preference objective that can provide social stability... and we are heading towards these, I think. Where we let go of objective morality and are left with the perspective of subjective preferences. From this, we can consciously find preferences that overlap and generate compromises where agreement is not there (if that is what we wish). Being acknowledged as being not how things should be, but how a group of people largely want them to be. And mechanisms for handling people who deviate in various ways from the largely openly shared preference is also something people can find preference compromises for amongst each other, while not obfuscating the issue with the intellectual baggage of moral/ethical philosophy and making it pseudo objective.
I think... many people are scared that the implications of there being no objectivity in regards to how people should be is that one no longer has any basis to punish people from deviating or to organize society in certain ways.
But we don't really need that. We have subjective motivation enough. We have preferences. We like things to be certain ways. And we can negotiate or force our ideals onto other people and ourselves without any objective justification, because... there is no because. We simply we can and want to. We can (almost) all have a degree of will to power for the sake of making things more as we want them to be than if we did nothing, because that's what's left when objective morality is not even a concept in a culture. We face that we have no justification wanting things to be a certain way, and we learn to accept this lack of justification as not being relevant, as not being necessary, and we are left feeling comfortable with imposing our ideals on the world simply because those ideals are what we like.