Which aspect of the make-up of our brains limits caring about many people?

GP is probably thinking of Dunbar's number[0] and making a distinction between caring concretely about specific individuals and caring more abstractly about the plight of many strangers. It's possible to "care" about the health and well being of arbitrary groups of people, but it really takes knowing and understanding their specific problems to make actual care effective.

[0]: https://en.wikipedia.org/wiki/Dunbar%27s_number

Dunbar's number has to do with the ability to maintain "stable social relationships", not "care". And I reject the notion that a recognition of shared humanity takes place in the abstract.

Please don't twist my words. I said nothing about the recognition of shared humanity, nor was I attempting to make any sort of deep philosophical stand. I was merely attempting to answer your specific question about the OP's viewpoint as I understood it.