I think there is actually a math answer. Kant's categorical imperative is an example of intersubjectivity, and it relies on a symmetry - that any given human can be substituted into any other position facing any other choice, in deciding what is just (we use tactics like juries to try to minimise impacts of picking an oddball).
We find the intersubjective stance also taken, in the 'obviously' not true statement in the declaration of independence, "all men are created equal". And in The Golden Rule, arguably the most culturally universal and longstanding moral principle. And present in Rawls' Theory Of Justice with the idea of the veil of ignorance. We are not in fact born equal, in a literal sense. And there is no veil of ignorance we will get shuffled behind, to choose our social structure unbiased. So why is this mode of thinking compelling?
Because intersubjectivity is the basis of communication and abstract reasoning, as discussed at How would you apply John Rawls "Theory of justice" to everyday decisions? Through engaging with other minds as 'swappable' with our own, we can share experiences, dilemmas, greatly expanding what an individual can experience & learn from. Fostering the ability to do this requires a shared sense of fairness and justice. We can see this in moral progress as described by Singer, as expanding the circle of moral concern. Universal citizenship, universal suffrage, ending legal slavery and sexism, is part of allowing all people to fully participate in the collective behaviours of language and culture development. Extending this to animals can help extend them and us, as discussed at Is our general level of abstraction in ethics hypocritical?
Just as children or the criminally inclined, don't invalidate the categorical imperative because it's about what is right, similarly with animals who haven't attained a cognitive level of responsibility. We have expectations on participants, and limit or exclude those unwilling or unable to take up responsibilities as well as privileges. That is about the stability of the system, and an essential precondition for people to participate.
A different perspective to come at morality from, is game theory. We can see if not lying is taken to be unambiguously correct, so no one checks, a single psychopath with limited intersubjectivity promoted to leadership, can persuade large groups to act against their interests. This is thought to result in a stable low percentage of psychopaths across all cultures, and they are over represented in company boardrooms, in general at cost to their companies. See The Pros to Being a Psychopath and Psychopathy in the workplace. Does this change what we consider fair and moral behaviour to be? No.
We can understand the social contract in relation to game theory, and it draws particular attention to the unit of selection. Discussed here:
Is the tyrannicide perpetrated by William Tell morally legitimate? The advantages of intersubjective behaviours must become less stable where a group is exploited, because you get a free-rider problem. Economists Wilson & Pickett provide the evidence base for this, in their books The Spirit Level & The Inner Level discussed at Why does poverty still exist in the world that discovered advanced technologies? I'd draw attention to the less well known 'social contract for the ages' of Burke, which highlights society as an intergenerational compact, discussed at Burke on the social contract. We can understand the implementation of this, with James C Scott's interpretation of 'metis' and 'cultural legibility', discussed at Philosophical framework for avoiding short-term strategies. We can see an example of how not providing justice and fairness, even where revolution is impossible, can lead to withdrawal of participation, in the 'lying flat' movement in China (contrasted with Hong Kong & the attempt to preserve accountable justice & politics by people with high levels of shared purpose).
Good communication, and good abstract reasoning, is founded on intersubjectivity. Adults grow accustomed to their society, but new generations always question it, emerging in an era of different technology & concerns, that challenges the legibility of previous cultural systems. Handing on systems, so as to avoid collapse (what Joseph Tainter describes as 'rapid simplification') & revolt, means appealing to the unborn - those literally behind a veil of ignorance. So these different dimensions of symmetry, of intersubjectivity, undergird our participation in something collaborative, culture, society, which is fundamental to being human and to our (so far) unique capacities, and takes us from solitary intelligences like bears and cephalopods, to the technology wielding creatures we see. When we exploit others, we make the system less stable, the integration less full, and the intelligence of our community is decreased.