Some people do have a love for our species. Most people only think about themselves and their immediate surroundings, so they don't "literally" care about continuing the species, but they care about love, sex, support, stability. In pursuing these wants, they contribute to continuing the species. This "big picture" view doesn't matter to most people as well, but indirectly it does through their actions.
It's just nature doing its thing. Think of wolf populations that kill elk, deer, and moose. When these populations are kept under control by the wolves, that means that they wont eat away all the plants. This means that plants are able to grow and flourish, which gives life to many other animals. Wolves don't care about nature preservation of course, they're hungry and just go hunting. But that's still what they contribute to. In the same way that most people might not think about the prospect of continuing the species, but they do it through their actions.