Here is the demonstration:
Does objective morality describe a single moral system shared by everyone? Answer: Yes
Does everyone share a single moral system? Answer: No
Objective morality is not the view that everyone agrees upon moral values any more than the objectivity of the shape of the earth involves a claim that everyone agrees with it. Not everyone does. This does not mean the shape of the earth is subjective.
Why should we expect an objective morality to manifest in the form of multiple competing moral systems accusing each other of being subjective moralities?
Human freedom. Now, why do you think we should expect universal human agreement on objective morality, especially since we don't get it on clearer truths such as the shape of the earth?
An underlying morality shared by every competing moral system has not been demonstrated to exist. However, for the sake of argument, the process of natural selection would sufficiently explain how such an underlying morality could have developed in us as a social species without any need for morality to be objective.
There are certainly arguments for it out there and I'd be interested in why you have rejected their claims, but if you feel it is tangential, I'm fine just assuming it is true for the sake of argument.
Why would the process of natural selection sufficiently explain the underlying morality, though? Is this claim falsifiable? Are you saying that different human groups could have evolved different morals (like other social species seem to, such as killing off all males once they have served a specific purpose), but it just so happens that we all evolved the same morals?
Not everyone's moral judgments are manifested as being objectively true by everyone else.
And we still have flat-earthers, too. This doesn't mean the shape of the earth is subjective.
Competing moral systems accuse each other of being subjective moralities.
Of course. That logically follows. Those who think the shape of the earth is objectively true and spherical will view flat-earthers as being subjective in the same way. My point is that most people naturally think there is an objective truth (and obviously usually believe they understand what it probably is). That's why we disagree with each other and talk about how people should act, appeal to some kind of standard others should be using to guide their thoughts, etc.
If subjectivism is true, the natural selection process answers that question for us.
Natural selection might be able to answer which subjective moral system an individual does follow, but it can't answer which one "should" be followed because there is no "should".
Any case that can be made will always be from a subjective perspective. What makes more sense for you might not make sense for someone else. The only way your particular system of morality will succeed is if it manages to survive the process of natural selection more successfully than all the others.
I agree, although I would say "make sense to
you/someone else." That doesn't mean there is no objective truth, though.
This is an invalid comparison because the knowledge we obtain through science is only conditionally accepted as being true. I described this in my epistemology.
And we conditionally accept our moral judgments as well. If new evidence comes up, then we should be willing to change our minds. That is what we should do with all of our beliefs, except maybe pure mathematics.