Understood correctly, social Darwinism refers as much to cooperation and community as it does to individuals looking out only for their immediate self-interest.
Our hominid ancestors learned to cooperate in order to hunt and raise families successfully. It’s true of other primates too, especially apes. Chimpanzees coordinate hunting and child rearing, share food, and demonstrate emotional sensitivities to other members of their troops. They work together to solve problems too, as this Youtube video shows:
We always strive to increase our chances for individual survival, so self-interest never leaves the equation. But the term “social Darwinism” or “Darwinian” behavior conjures up images of purely uncharitable egoism. This is a harmful misunderstanding of Charles Darwin and evolutionary theory that is often used to discredit the scientific truth of social relations in the human and animal world.