This may sound horrible, but sometimes I think that people care too much because people like to label and categorize people as much as possible. If someone can label your personality, then they can either validate or invalidate what you say, mean, mannerisms, and they may take you more seriously (or less) depending what your type is. I you're mistyped, then they can't treat you according to a particular label and point the finger at you. . .they can only point the finger at themselves for the way they disregarded, invalidated, etc., you, and many people don't like to be wrong. The problem with applying a label to someone, such as an MBTI type is that it allows some people to judge and stereotype you, and they may treat you according to the description they read about your type, and this may allow them to treat you rudely and seem to get away with it.
I'm not saying everyone is like this, because many find their type just to know more about who they are, allow it to assist in guiding them, or to understand people better (without the rudeness and stereotyping or judgment). . .not everyone has a negative motivation behind the typing, but some may. It's pretty much the same with any type of label, other common ones being zodiac signs, natal charts, and so on. Too many expect you to fit the exact description and characteristics of the label and leave little to no room for individuality. Sure, many people may share the same category (MBTI type, enneagram, zodiac sign, etc.), but they're not all the same in personality, interests, etc. 100%. People may do, act, feel, etc. differently than some of the things described in their MBTI type, and some may not.
We just need to keep an open mind and make sure we don't hold onto the labels in a negative way as a tool to pass judgment on each other. That's why I feel some people freak out if they think someone is mistyped. . .they don't like being wrong, it isn't easy to stereotype someone that doesn't clearly have a definite type, and perhaps they think that people who list themselves as a certain MBTI type but may not actually be that type, are posers. Some people take it way too seriously and make it sound like each particular MBTI type is it's own separate gang, blood in-blood out. I haven't met people on this site yet like that, but I've seen them on other sites unfortunately. I'll be the first to admit that I tested and got INFJ, but I feel I've somehow been mistyped. Maybe I haven't, but I'm just not sure.