There is an old Buddhist saying that my teachers would remind us about that caring follows knowing. The more we know about people the more we care about them. The corollary is that if we want to others to care about what we care about, they must first feel that we genuinely care about them.
The key word here is genuinely. Genuine caring transcends treating others as a means to our ends.
When we genuinely care about others we care about the stories they are living in present tense, because ontologically, we are our stories.
We take time to reflect with them on their dying parents and friends. We take time to listen to the joys of their children's humble and heroic journeys. We take time to resonate with their daily struggles and hopes. This is the character and power of caring.