The problem comes from the culture; certain cultures identify success as the core value of a person, so people tend to identify their identity with the product of their work.
It's more than some "important"; work is how people [with this attitude] values theirselves.
Keep in mind that if you grow up pushed to be the best at school and then at work, there's nothing really meaningful in life outside those areas.
That's where the false dichotomy "being great vs. family comes". Essentially, it's perceived as having something that makes one happy at the perceived cost of "being a nobody".
At the extreme of this attitude the is Japan, where work is taking over the sexual life (there was an article some time ago in HN).