If you had any way to back up your opinion with logic, we would have something to talk about.
I may be misunderstanding you, but I think you're making an error in how you view moral decisions.
You seem to be saying that we begin with a philosophical premise, and one of those premises is that we do what feels right to us, but there are other premises we may adopt.
However, in my personal experience, and in the research I've read about the brain, and in my professional experience and reading of research on decision-making, I don't find that to be at all true.
Rather, what seems to be the case is that we always do what we feel like doing. We encounter dilemmas when we have equivocal feelings regarding our choices.
So if I live in a society which, for example, puts people to death for being homosexual, or for publicly disagreeing with the government, or for rejecting the state religion, then if I am emotionally ok with all of that, I have no moral dilemma. I'm a good citizen and I go on with my life.
However, if my genetics and development have given me a brain that's wired so that I'm emotionally distressed by all of that, then I have what you might call a moral choice to make.
Do I suck it up and toe the line, regardless of those negative emotions? Or do I try to change the status quo in order to move into a psychological space that I can more easily live with -- even if doing so puts me in physical danger?
You see, it's always about satisfying our emotions and figuring out what we have to do to get into an acceptable emotional state.
I think all Harris is saying is that you're going to have a different experience if you come from a religious perspective, or a selfish perspective, or a scientific perspective, or what have you.
So it follows that there must be a scientifically oriented, or scientifically informed, morality. Just as there is a religiously informed morality. Or a morality informed only by one's own immediate gratification (e.g. the sociopathic morality of Ted Bundy).
If you honestly believe that the Bible or the Quran is the Word of God, then that has a profound impact on your state of mind when deciding questions such as "Should women be subservient to men?"
Your community's interpretation of those texts will also have a lot to say in how you feel about that question.
But if you're coming from a scientific frame of mind, the interpretations of those texts by any community has no bearing. And that changes how you feel about those issues.
Yet in all cases, it comes down to how you
feel about the alternatives, and what you can do that you think you can "live with".
Harris would say that a perspective based on science, rather than on interpretation of religious scripture, is superior because that point of view is more accurate when it comes to modeling reality. And I agree.
But you don't even have to agree with that point in order to accept Harris's central premise, which is that a science-based approach to moral questions is indeed possible.
You may well disagree with his conclusions about particular questions (as I do, as well) but I'm not seeing any evidence that he's wrong about the big picture.