Moral objectivists correctly argue that the apparent unreliability of our sense of right and wrong does not falsify the case for an objective morality. This can be seen by considering spatial orientation as an analogy. While flying an airplane, I can become disoriented, and not know which way is up or down. However, the fact that I can become disoriented, does not mean that there is no up or down, only that I am confused as to which way is which.
I don't think anyone attacks moral objectivity on these grounds, but I found it instructive to consider the differences between moral and physical sensation.
Our physical sense of orientation correlates feelings in our inner ear, our vision, and our sense of touch. Whether we are standing or ascending a rope, our sense of touch conveys a direction. It feels different to lie on an incline face up versus face down, or uphill versus downhill. Our visiion is somewhat less reliable, but, most of the time, the world looks different when we face up versus face down. Our inner ear primarily senses changes in orientation rather than orientation itself. Hence, it seems that up and down are primarily defined by our sense of pressure and touch, and that vision and balance provide additional guides to orientation. From this information we create models of the physical world that relate the positions of objects, and the forces we will experience given velocities and accelerations.
Our theory of spatial orientation is more than just physical sensation of directional pressure. The formal model of which way is up relies on a deeper model of the shape of the world, whether it be mostly flat, or like an M.C. Escher painting. Which way is up is based on the model, not just the sensation, because the model is a more accurate guide to future sensation. That is, the model is predictive.
Now, let's consider moral theories. Our physical senses serve to tell us what situation we're in. We can see a pocket watch lying on the sidewalk. Our physical theories tell us what will happen if we take the watch for ourselves and hold it or trade it for personal gain. Our theories also tell us what will happen if we try to return the watch to its owner. In each case, we also get a moral sensation. The former act feels wrong, and the latter act feels right. The question is, what do our moral feelings predict? What do they add to our physical model?
Our moral feelings are predictive of just two things. First, our moral feelings may predict how we will feel in similar situations. Second, they may predict how other people might feel in similar situations, assuming they are like ourselves. That is, our moral feelings build a model of ourselves, not of anything else. All other prediction is part of our physical model.
This is much like art and gastronomic taste. All nutritional value being equal, we may feel differently about cherry-flavored candies than lemon-flavored ones. Such differences in taste inform us of nothing but our own gastronomic wiring. We might know that we prefer lemon to cherry, but that's not a statement about lemons and cherries per se, only about our subjective tastes for them. Likewise, two paintings with equal informational content, and equal material content may stimulate us in different ways. This reaction is about our own aesthetic tastes, not about something external to physics. It's predictive of nothing except how our subjective aesthetic tastes might react to other paintings.
Back in moral terms, knowing that we prefer not to take someone else's dropped pocket watch leads us to the model that we prefer not to take what doesn't belong to us. That is, moral theories are generalizations about our individual, subjective feelings on moral issues. While I assert that I feel that theft is wrong, I wouldn't call such an assertion an objective truth about anything but my own feelings.
Like other theories, moral theories can be wrong. Suppose my initial moral theory is "finders, keepers," and I take the dropped pocket watch. Later, I learn of the tragic effect the loss had on its former owner. This effect is a physical one, and I update my physical model accordingly. Given my new knowledge of the scenario, I might then regret my decision not to return the watch. In retrospect, my moral decision was wrong, as perhaps was my "finders, keepers" theory. However, the result of my moral theoretical revision is not deeper knowledge of something external, but a more accurate account of my own moral sensitivities. I have changed the scenario, and my feelings about that scenario change accordingly.
Thus, when examined carefully, we find that morality fails to be objective in the same way that physical sensation is objective. Our moral feelings can be used to construct a model of our personal tastes, and nothing more. Such models are not about anything external to ourselves, but only about our patterns of individual, subjective reaction to external situations.