Conflicting Viewpoints

In my Environmental Policy class yesterday, we talked about the concept of equity and how, if we all understand equity to be the same thing, then why is it that we constantly fight over which policy best achieves this end? Well, then I found out that we don't all view equity the same way, or rather, when making policy decisions, people tend to focus on different aspects of equity.
For example, there are those who concern themselves with defining who is part of the groups in question (ie. who is included and what makes them a candidate for inclusion). This would mean the difference between policy operating on rank, on operating on merit, or one that revolves around a group (are a millionaire minority and a poor minority treated the same, because they're both minorities?). Then, there are those who focus instead not on the "who" but on the "what." Should everyone get the same, or should distribution of benefits be based on value to the individual. Two people can be given the same coat, but if it's a good fit on one person and too small on the other, then is the policy promoting equity? Finally, there are those who instead focus on the process of distribution and whether or not that is fair. They propose that, regardless of the outcomes achieved, if the process is fair, then equity is promoted. In a democratic capitalist society, we often fall back on this reasoning. Not everyone will be president, but everyone has a chance, right?
I don't think that equity is the only aspect of society where we all say we want the same thing, but don't know for sure if we regard what we want the same way. Working with people in different environmental groups has opened my eyes to this quite a bit. We all "love nature," yes, but this guy likes it because he likes hiking in it, and wouldn't see the value in promoting wilderness that can't be accessed and enjoyed by humans, while this lady thinks we should protect nature as a way of conserving natural resources for future generations, not necessarily because she thinks these resources have value in themselves. It's tricky, but does explain why we have so many arguments when we claim to want the same things.
Can anyone else think of other areas where we seem to have this problem?