For the same reason every other being lives of course, survival and reproduction. Mastery over our environment
Even a tree or a simple blade of grass contributes to those examples
edit: perhaps those too could be categorized underneath self interests? if so I'd point out things like bees, ants or fungi that contribute to a hive mind of sorts, working for the greater good
"Whether people know it or not, they're all part of some trial to test and improve the odds of survival of the species. No matter where we're at"
That perspective imbibes purpose itself. Without that perception superimposed on "reality," what we are left with are chemical reactions and laws of nature...matter behaving as it must, all bits of the universe acting in intertwined unison. From that vantage point, "survival of the fittest" seems more a part of the largest domino chain ever set (the universe), and less like a struggle with any defined function.
I am not disagreeing with most of what you are saying, only I do not believe genetic continuity is inherently purposeful.