Ultimately morals originate in values, which originate in instinct and or nature. There is naturally a lot of reasoning, inference, and trial-and-error along the path in coming up with said morals. The differences you see between persons and groups result from differences in both nature and nurture, though arguably mostly the latter since most humans have a lot of nature in common.
Even a simple negative feedback mechanism, like a thermostat, can be said to have values. For example, in the cold of winter, opening a window could be deemed immoral to the instinct or nature of the heater since it "wants" to maintain a certain minimum temperature.
For absolute moral subjectivism to be rational, there would have to be little if any shared desires or values between the beings in question. We know this not to be the case when looking not only at human society, but at nature in general. Humans have plenty of needs and wants in common, and this applies to most if not all other known life.
On top of that, even from the perspective of passing on one's genes, humans and many other lifeforms here have plenty of genes in common; so being at least rudimentarily courteous to our neighbours has plenty of benefit if our genes are to be valued.
Moreover, the complex ecosystem around us has a lot of interdependence, where any significant interruptions to other beings can come back to us. Hence, we have inherent reasons to care about others, including those seemingly quite distinct in form and function.
One thing about morality is the more you think about it, the more you see the vast interconnectedness of our actions and their effects on one another, including back unto ourselves in some, often indirect path. Maximum viability of the species and biosphere depends on rational regard for these interconnections. Denying our interdependence and personal role in the greater picture is collective neglect, perhaps suicide. The more powerful and pervasive a creature, the truer and faster this holds. With strength comes responsibility.