The section on in "The Oxford Reader: Schopenhauer" states:
If there is a part of compassion in everyone's psychological structure, what remains? Schopenhauer's complete answer is as follows:
The three basic ethical motives of humans—selfishness, malice, and compassion exist in different and vastly varying proportions in each individual. The motives will act upon people according to these proportions and lead to their behavior. (On the Basis of Morality, 192)
Selfishness is "immense" and "natural":
Every individual, small enough to be almost zero in a vast and boundless world, makes themselves the center of the world, placing their own survival and well-being above all else. In fact, from a natural perspective, they are prepared to sacrifice everything for this; to allow themselves, a mere drop in the ocean, to live just a little longer, they would be willing to destroy the world. This tendency is selfishness, which is essential for all things in nature. (The World as Will and Representation, Volume 1, 332)
Selfishness so greatly "overrides the world" (On the Basis of Morality, 132), that without the constraints of law represented by the state machinery, individuals would be drawn into a war of all against all (On the Basis of Morality, 133). All of this implies that actions motivated by the well-being of others should be not only rare but also impossible due to their contradiction with our nature. Schopenhauer had to admit that compassion is an enigma in ethics. The only thing he could say is that compassion is a primitive anti-selfish characteristic that exists in us as a pure fact. But how compassion can "reside within human nature" (On the Basis of Morality, 149) is a profound mystery, as humans are a natural expression of the will to live's selfishness.
So let me explain, how can humans have a sense of compassion? There is a saying, "When the rabbit dies, the fox mourns; creatures grieve for their kind," which does not mean that a fox will truly mourn a dead rabbit, but rather metaphorically refers to the sadness caused by the death of companions or kindred. Humans have a sense of compassion because they see in their kind the potential for experiences that could befall themselves; their imagination allows them to place themselves in the situations faced by others, thus suffering mental anguish, which leads to the emergence of compassion, feeling sorrow for the suffering of others. This is similar to how we immerse ourselves in movies or artistic works, identifying with a character and sharing their joys and sorrows; we say this is because we have the ability to empathize, or the ability to step into another's role. The premise of this ability is that humans possess imagination. Therefore, what humans feel compassion for is actually an imagined version of themselves.
Reflections on reading "The Oxford Reader: Schopenhauer"