That is incredibly selfish. Sometimes the person doing the lifting is the one being "brought down", so you're essentially depending on the fact that people are less selfish than you for this to work. Like anything taken to the extreme, this extreme individualism can only be harmful.
It also avoids the common human-behavior anti-pattern where two people remain in a mutually self destructive relationship because each is under the delusion that the other can't live without them.
There's a difference between supporting someone through their difficulty and someone who is not supporting you, whether that means (consciously or unconsciously) belittling, undermining, or dismissing you or your ideas, or just not meshing well or productively with you.
This isn't exactly a new idea. http://bible.cc/proverbs/27-17.htm