I’m going to share with you a concept that will very much enlighten this question.
It is the concept of the Hierarchy of Needs. The premise, proposed by a very interesting psychologist Abraham Maslow, is that humans need to fulfill a certain amount of needs before advancing to the next tier and fulfilling those.
The malnourished kid with AIDS is still working on fulfilling their most basic needs, the physiological rung. They are trying to secure food and shelter and water and not be diseased by flies and what else. When they do secure this, they will move on to fulfilling their next rung of needs, safety, then love and belonging, and so forth. Anyone born in such a place, namely parts of Africa, stands a high chance of starting at the bottom rung in life.
Somebody in a first world culture though, they start well into the middle of the pyramid. Their family structure provides the first and third, the government and society provides the second and various overlaps on the first. Thus a person can start immediately working on the fourth level, self esteem, respect, achievement, as well as the fifth level, being creative, solving problems, using logic, etc.
What does this have to do with suicide? I believe that thoughts of suicide, or thinking that can lead to thoughts of suicide, start occurring around the fourth and fifth levels. Simply put, one is too busy trying to survive (finding food, reproducing) to care about questions such as “Why am I here? What is my purpose? Will I ever be happy?”. But these thoughts are much more likely when you start out halfway up the pyramid.
Of course, it really is all relative. If Africa were to become a first world nation, their people would likely sometimes turn to suicide as they too start questioning their existence and purpose.
So I do not think it is a product of our culture at all, but a product in our nature of being huge brained creatures. We are built to think, and sometimes our thoughts can lead us down interesting or dangerous paths, especially if we are under some type of chemical disruption (such as depression, drugs).