I hypothesize that humans have only so many shits to give.
Some of us start out with more inherent ability to care than others do, but however much caring you’ve got in you, there’s probably not a lot you can do to increase it beyond that basic amount.
What you can do, however, is shift it around.
If things are going really badly for yourself, you’ll dedicate most of your energy to yourself–dealing with sickness, job loss, divorce, etc., leave very little energy leftover for anyone else. You are simply empty. You have no more shits to give.
If things are going badly for someone close to you–family or friend–you’ll dedicate much of your energy to them. A sick or suffering child, for example, will completely absorb your care.
Beyond your immediate circle of close friends and family, the ability to care about others drops dramatically, as the number of others increases dramatically. You might give a suffering acquaintance $5 or an hour of your time, but it is rare to otherwise go out of one’s way for strangers.
There are just way too many people in this category to care deeply about all of them. You don’t have that much time in your day. You can, however, care vaguely about their well-being. You can read about an earthquake in Nepal and feel really bad for those people.
One of the goals of moralists and philosophers has been (I think) to try to increase peoples’ concern for the well-being of others. If concern for others can actually be *increased*, then we may be able to care about ever-bigger groups of people. This would be especially good for people in modern society, as we now live among millions of people in countries of hundreds of millions on a planet with billions, while possessing nuclear weapons and the ability to destroy our own environment, it is pretty important that we feel at least some vague feelings of responsibility toward people who are not within our immediate friend/family circles.
Even if moralizers and the like can only cause a small increase in the amount of caring we can do, that still could be the difference between nuking a million people or not, so that’s still a valuable thing to try.
(Note that this kind of large-scale concern is probably entirely evolutionarily novel, as the ability to even know that people exist on the other side of the planet is evolutionarily novel. Most people throughout human history lived more or less in tiny hunter-gatherer bands and people not in their bands were basically enemies; it is only in a handful of countries over the past couple thousand years or so that this basic pattern has shifted.)
But to the extent that the number of shits we can give is fixed, we might end up just shuffling around our areas of concern.
And doing that seems likely to be prone to a variety of difficulties, like outrage fatigue (being unable to sustain a high level of caring for very long,) missing vital things that we should have been concerned about while being concerned about other things, and fucking things up via trying to fix problems we don’t actually know the first thing about and then getting distracted by the next concerning thing without ever making sure we actually improved things.
Well-meaning people often try hard to care about lots of things; they feel like they should be, somehow, treating others as they would themselves–that is, extending to everyone in the world the same level of caring and compassion. This is physically impossible, which leads to well-meaning people feeling bad about their inability to measure up to their standards of goodness. As Scot Alexander points out, it’s better to set reasonable goals for yourself and accomplish them than to set unreasonable goals and then fail.
My own recommendation is to beware of “caring” that is really just social posturing (putting someone down for not being hip to the latest political vocabulary, or not knowing very much about an obscure issue,) or any case of suddenly caring about the plight of “others” far away from you whom you didn’t care about five minutes ago. (Natural disasters excepted, as they obviously cause a significant change in people’s conditions overnight.) Understand your limits–realize that trying to solve problems of people you’ve never met and whom you know virtually nothing about is probably not going to work, but you can make life better for your friends, family, and local community. You can concentrate on understanding a few specific issues and devote time and resources to those.