Another option might be insanity of one side in a controversy although that will not be a problem so terribly often, one would hope. Finally, one possibility that I think is under-appreciated is different levels of maturity. For example, it is a sign of immaturity to prefer immediate gratification over greater deferred gains, so a conflict over two possible courses of action could be simply based on one person being more mature than the other.
Although I do believe that there is no objectively, universally deducible system of morals, I also think that we humans share many of the same instincts and interests and could potentially agree on more ethical questions than we generally manage to do, and that the problem has its roots at least partly in different levels of maturity. It seems fairly clear that there are different stages of moral development that a person can go through as they mature:
- They are completely self-interested and lack empathy. Rules are only followed because of the fear of some form of punishment (ranging from the mild disapproval of authority figures to severer penalties). It is perhaps an oversimplification to assign this state to babies and very young toddlers but not by much. It is certainly also the stage at which most house cats appear to be stuck: once you turn your back, they do what they see fit.
- They know that there are rules and that one should follow the rules, and that is it. In hindsight it was fairly clear when my daughter had reached that stage of her personal development.
- They understand that rules exist for a reason, and that what really counts is whether the intention behind the rules is being achieved. Some rules may be in conflict with each other, and knowing what they were written to achieve allows you to figure out which of them to break in such a case. In fact some rules are silly and can be ignored while others are crucial. A clear example would be rules whose real purpose is to minimize harm to people; if you can minimize that harm better by exceptionally breaking one of the rules, so be it.
- Finally, they start to question how the intention behind the rules can actually be justified. Who says that achieving accident-free traffic flow, minimizing harm or suchlike are actually the things we should care about? Can we justify them from first principles? Some people might fear the collapse into nihilism here but really this stage of moral development is both necessary and liberating. Leave nothing unexamined. (And yes, ultimately we make our own rules, but that is how it has to be because they are for us and about us and by us. Pretending that the rules came from the gods, for example, is merely a self-serving lie because they were really created by humans. If we all acknowledge that we have a better basis to improve them.)
Many more are stuck at the second stage, the one of blindly following rules. This is behaviour often associated with bureaucrats although that is perhaps unfair as administrations are built precisely to foster it. More importantly, it is obviously what we might generously call the moral philosophy of religious fundamentalists: X is bad because God says so, look it's here in my holy book. Ah, but X does not actually hurt anybody, so who cares? Doesn't matter, God says X is bad, that settles it. The same is true for many very conservative people who value stability over all and fear that not following the traditional mores of society will result in whole-scale societal collapse (instead of merely a similarly stable and healthy society with different mores).
It is because large numbers of people are stuck at stage 2 in their moral development and many others have advanced to stage 3 that moral controversies (the "culture wars" in American terminology) are so intractable. If one side thinks that rules are rules are rules, and that is it, and the other side thinks that rules are only tools that need to be changed if they don't achieve some more transcendental goal, then it is hard to ever reach an agreement.