@maxdancona,
Philosopher Massimo Pigliucci, host of the podcast, Rationally Speaking, has some ideas on this which I will try to summarize. He says that moral reasoning is similar to, though not exactly the same as, mathematical reasoning. Both depend on the premises that you start with.
For example, if your premise is that the ultimate moral value is to cause more happiness for more people, or to fulfill people's preferences, as opposed to causing more unhappiness, then Utilitarianism is probably going to seem very reasonable to you. If, on the other hand, your basic value is to respect individual rights and autonomy above everything else, then Objectivism is going to suit you. If your value is to obey the commandments in the bible, or the laws of the land, or otherwise follow what you conceive of as a god's or a government's instructions, then you would probably adopt Deontology for your moral framework. If you value character development and cultivation of personal excellence, then you would likely prefer Virtue Ethics above the other moral philosophies.
If the scope of your moral concern is your immediate or extended family or a close-knit group, then you may reason that you should treat those around you well, and let others fend for themselves. Some may choose to extend the "circle of moral concern" (see Peter Singer) to other races, nations, and even to animals.
The reason there is no one, single "best" moral philosophy is because we all start with different premises, and those premises are based on our value systems. There is no logical proof that one value system is superior to another. Values are givens - they are the axioms and premises of morality. Sometimes we choose our values, but frequently we simply have them, just as we have tastes and preferences for different music or food - they precede and trump any sort of logical justification.
Ethics is really, then, a form of applied logic. You can start with different premises to come up with completely self-consistent, coherent, moral frameworks, none of which is superior to the other but offer different solutions to the "moral problem", and none of them refutable on purely theoretical grounds. We can easily see that different branches of geometry are not superior or inferior to one another, but reach different conclusions because they start with different axioms. We can see that one type of geometry may be far more useful and applicable in the real world in which we find ourselves than another, and some forms may have no practical use at all. The same is true of moral systems. Although we may not be able to apriori judge one superior to another, some are very probably far more able to be successfully applied to human and social environments than others.
Regarding "objective morality" - the existence of moral standards independent of humans and their moral preferences as opposed to purely relativistic morality - I think that is a false dichotomy. I reject it for the same reasons that I would reject an argument in favor of a one, "true" geometry. The choice of a geometry or of moral system all depends on the starting premises. Euclidan, Hyberbolic, Riemann, and other geometry systems are all "true", but each starts with different axioms. The same idea applies to moral systems. They are "true" in the sense that they each follow logically from their founding premises - given their starting points, they are internally consistent, coherent, and well-defined. In ethics and morality, there probably is no fundamental value or axiom that is clearly superior to the others. There certainly are, and have been, unworkable, low quality premises, such as "murder and mayhem is a core value", or "exterminating all undesirable people is virtuous". There are, and have been, some people and nations that held these values. But values such as these are incapable of serving as the foundation of a coherent, sustainable moral system. In those unbalanced moral systems, the value that works for you today can be turned against you tomorrow (you may wake up one day and find yourself to be an "undesirable"). Core values such as these lead to degenerate and failed moral systems, full of contradictions, are self-limiting, and which cannot allow the people who practice them to even survive for the long term (Nazism, anarchy, and vicious and bloodthirsty regimes in some less developed countries, for example). Likewise, one could (and this has happened before) devise geometric axioms that are mathematical dead ends incapable of producing a useful geometry, or are incapable of application in the real world of human concerns.
There are many internally coherent moral/ethical systems that don't suffer from internal contradictions and which serve the goals which are embedded in the premises that underlie them. However, moral systems have to be anchored to the factual aspects of human nature, and the nature of society. If they are not, then they are entirely abstract and irrelevant to human interests. They become the equivalent of a mathematical model which has no application in reality. You can do math in that system, but you can't do physics with it. Ethics, as an applied discipline, has to deal with human beings and human culture, not with abstract notions. This requirement reduces the set of viable ethical systems down substantially, but still leaves room for a large variety of very diverse approaches. There are a number of alternatives that are perhaps equally reasonable and perhaps equally defensible. But those alternatives are not infinite in number - they don't represent the entire set of logical alternatives. They are tethered to the actual realities of what it means to be a human being living in a human social environment. If we were birds, or wolves, or any other type of being we wouldn't even be having this conversation, or if we could converse about this, our radically different natures would cause us to adopt a very different type of ethical system.
