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The more people care the faster we learn about it, the more discoveries we make at sooner times. Hence human beings should care about it. Anything to push humanity forward is a good thing. We should all care enough to at least ponder it every now and again. Maybe it leads you to a career in science.
Humans should not really care about whether or not there is a black hole information paradox. For the most part, most people will never be effected by a black hole information paradox, and there is not threat of anything bad happening. There are only a few people who even know what this is.
Most people do not need to worry about abstract philosophical problems. The paradox involving black holes is far to separate from everyday life for most people to care. This is question for philosophers and perhaps astronomers. Most people do not even have a clear idea of what a black hole is.
I believe the theories surrounding black hole information paradox is important and I don't think it is fair to say that all humans should basically ignore this problem. The topic is fairly convoluted and difficult for the common person to understand, so I find that it is best for a small section of the population, namely scientists in the field, to continue studying this paradox.
Black holes are interest phenomenon for scientific study that may eventually provide information that is key to figuring out space and planetary design, including design relative to our own planet. Most humans, however, will never have a need to develop advanced understanding of black holes. There is not one near enough to our planet to be relative and, thus far, it has not been established that they can develop suddenly. So understanding how they pull matter into them is of considerably more value to scientists than the average person.
In the long run it does not meake a difference if there is a black hole information paradox. It is not going to change anyone's life. Topics like that though can be fun to discuss and think about because in the end there is no proof either way so best arguement wins.