The individualistic self is independent. Think of separate circles in a space. The collectivist self is interdependent; think of one circle, interlocking with many others. Relationships and ties with others, such as "daughter, student, granddaughter, wife" are very important and parts of self are seen in the others one sustains relationships with, and the quality of those relationships.
I wish I had time to think this through before posting.
I think the big problem here is that the "individualistic" Western culture has lost the sight of these connections. People perceive themselves as independent from others, but that's crock. We are constantly shaped and defined by people around us, whether we choose to or not. We need others, to support us, to compete against, and yes for us to support them.
A self-centered view of the world, where one's primary goal is to realize one's "potential" to one's own satisfaction clashes with the reality of human nature as a social animal. In the process of evolution, a species where each individual is relatively weak compared to lions and tigers (and bears) became a top predator through cooperation. Our greatest adaptations are the intelligent brain and the ability to communicate effectively (almost ran into a Spanish Inquisition trap here. "Among our greatest adaptations..."
). The brain takes a long time to mature, and the human offspring is virtually helpless for years, which ties up a lot of resources of the group in childbearing and childraising. This makes the individual's life precious and valuable to the group. We are wired to both contribute to the group and to crave the group's support and approval.
The instinct of continuation of the species is perhaps the strongest one, overriding even self-preservation. I expect that most grown-ups would risk their life without a thought by, for instance, rushing into heavy traffic to grab a child.
Ironically, the Western individualist culture also clashes heavily with the demands of the prevailing religion, which focuses on the pefecting the spiritual self and negating the physical. Vison has expressed this much better than I could.
My main problem with many belief systems is the insistence on self-abnegation.
Since it is impossible to "give up" self interest, the poor suffering pilgrim is awash with guilt, thus proving that she is a bad person and thus is a sinner and on and on we go.