I believe the answer to this question lies in the fact that humans are diverse. Diversity is what has caused humans to be as successful as we are and as has also caused humans to generally hate each other or have opposing views.
Everyone has their own opinion, but a lot of people don't realize that a lot of the things they accuse an opposing party for is what they do themselves. For example, not saying anyone in particular does this, but generally people would accuse a furry hater of hate, but at the same time the furries themselves will hate the furry-hater. The furry-hater, as well as the furry, simply has a view on the sub-culture, and a furry has a view on the sub-culture of a furry hater. Now you might say that the views are different because a furry is simply enjoying their own life-style without interfering with anyone elses lifestyle, while the furry hater is actively trying to change somebody elses lifestyle. This is kind of true, but you have to realize that to a furry-hater, acting like a furry around them is AGAINST their lifestyle and by saying "simply ignore it" or "enjoy it" you are actively trying to change their lifestyle like they are trying to change yours. Now if you say that simply being around someone who acts different doesn't affect your lifestyle, I'd offer the thought experiment of what if a couple had sex right in front of you in a public place. No doubt that would make you quite uncomfortable because by doing that they are effecting your lifestyle.
In no way am I condoning furry hating, I dislike the idea of furry hating personally and i think it should never be done. But what I'm highlighting is that when ever you have two groups with opposing views, from a completely third party perspective, these opposing views will both be, essentially, equally valid (when they have to do with morality and social issues especially). It's up to social processing, culture, possibly genetics and up-bringing that changes which viewpoint is considered valid or better, but because these things change due to diversity, you will get different viewpoints and because both parties have valid reasons in believing in these viewpoints (at least relative to themselves) they will see the other party as illogical and will find the other party tackling their ideals which causes hate.
As for your quote, I would say it isn't necessarily true. "Every action has an equal and opposite reaction", in terms of society I would have to disagree with that statement. For one thing, some issues are very complicated and there might not necessarily be just two viewpoints on the issue that are directly opposite each other, as well, it's hard to define in some cases whether two viewpoints ARE the direct opposites of each other. It could be argued though that theoretically there would be one person, somewhere, that would always believe the opposite of what someone, somewhere else, believes. So the more important thing is equal and generally, people believe things in varying degrees of magnitude. So I don't believe that EVERY action would have a grey area, though of course it isn't necessarily UNTRUE because there is a theoretical situation where there is a person who believes in the exact same magnitude, in opposite direction, to a belief as you. However, all of that seems unlikely, so I'd say the statement is unlikely but is not necessarily untrue.