In my experience, people who proudly evince callous indifference to the suffering of others are usually one or more of a) privileged, b) sheltered, or c) quite young. In other words, naiveté. Rarely is it due to actual, willful malice. So yes, I meant it.
My answer was a rarely honest report on my actual interactions with the world. We live in a time where give well estimates something on the order of a few thousand dollars can save a life, through malaria donations etc. How much of my income do I actually donate to these people? About 5% I guess. How much would I pay for my own longevity? Way more than that.
Would you? If given the option between extending your life to the age of 200 through yearly payments of $10,000 -- or instead donating that money to save countless lives a year, which would you do? Maybe you would donate it, I don't know you, and I won't presume the answer. But is it a callous indifference to pick yourself instead? Maybe it is, and if so, I'm callously indifferent.
We could play with those numbers though, to see how you would value an additional year of your life vs. saving a year for one of the world's poor. Would you value them the same? It's only natural to value your life, and your family's life, higher than others. What's the number where it's not callous indifference? It's worth thinking about, although I don't think the answer to these questions is pure nihilism or anything, we should definitely work to improve the world, and certainly donate more than we do now.
But the point I'm arguing against is that this doesn't mean we also need to put on hold work to improve longevity of our lives.
(It's also worth noting that this entire argument is far more nuanced and second order than the simpler one I offered above, which is that holding this business to a different standard than, say, Facebook, doesn't make sense. Any time you choose to start a business or work, you can always instead choose to go work for a firm with a mission to help the world's poor.)
As for your previous claim that it's in my direct interest to support the world's poor, that's true, but it's also not weighing it against the appropriate benchmark. The appropriate benchmark being what else could I do with that money that would benefit me.
Here's what I don't understand. You are trying to convince someone that they are being "callously indifferent to the suffering of others" by telling them that "their utility is correlated with the utility of a poor person". Sounds like you both seem to have comparable goals, just that you believe that your "way" of accomplishing the goal is superior (i.e. help others to help yourself, rather than just helping yourself)