Even if one doesn't "naturally" care about others, it's also true that even from a totally selfish perspective it still kind of pays dividends to be a good person, be concerned with the welfare of the people around you, and build interpersonal connections.
There's limits to that, for sure. There are a number of biological bases for empathy. And being biological, it stands to reason that different people will have different capacities. But, it also certainly feels like a skill.
Here's another angle. A lot of people, perhaps maybe a lot of engineer types, struggle with empathy because the needs and wants of others just feel like a confusing sea of infinite possibilities. But here's a trick. At any given moment, any given human being is probably just trying to fill one of the needs on Maslow's Hierarchy of Needs.
Most people like watching movies or reading books. Other people are the main character of their own life, and I think you can learn to enjoy learning about them.