For instance, I am a dog person and my girlfriend is a cat person. Occasionally, we start to debate the relative merits of each. And there may in fact be one which is in general "better"; after all, most people would agree that dog ownership is better than man-eating tiger ownership. But since we both recognize that dog and cat ownership is a rather silly thing to get upset about, we don't.
On the other hand, politics (for example) are considered to be important. And while we may realize that it's nearly impossible to find a "right answer", that our discussion will likely lead to nothing, etc., we don't feel silly getting upset about it. That, combined with our identity-based connection with politics, leads to flared tempers and out-of-control discussions.