I think you are blurring together two different types of people. Rebels often do what they do because they do care. They see suffering in the world, and they think it is the rulers, the system or tradition, etc, that is responsible for this, and sometimes they are even idealistic enough to set out and change it for the better. (they think it is something "outer" forced upon people that makes them cruel or at least blind to the suffering of others, for example, and these "others" are usually the minority the rebel identifies with in some way).
rebel (noun)
1. a person who refuses allegiance to, resists, or rises in arms against the government or ruler of his or her country.
2. a person who resists any authority, control, or tradition.
A rebel would say that the always unhappy, irritable, selfish, inflexible person who does not care about the feelings of others is the product of modernity/capitalism/consumer society/colonialism/globalisation/etc (pick your choice). If we change the system, people will be happy, humane, tolerant, caring, etc.