From the comments of this old LessWrong post, a jewel by Said Achmiz:
Let's say that after diving into the pond to save the child, and ruining all of my clothes in the process (which still don't add up to $2000; no complete set of clothes I own adds up to that much), the very next day, I am walking across the same pond (in new clothes), and [a] kid's drowning again.
So of course I save [them] again and am out a bunch of money/inconvenience again.
And then the next day another kid's drowning there.
And the next day.
At this point, most of my clothes are ruined, so I'm pretty upset. But more than that: I'm angry. Who the heck is letting these kids play in the pond? Where are their parents? Shouldn't someone put up a giant sign that says "DON'T PLAY IN THE POND, YOU IDIOT KIDS", or a fence, or an electrified fence? Is relying on strangers walking across the pond and ruining their clothes to save these hapless kids really the best solution to this problem? Why am I on the hook for this?
At that point, I might complain to the police, say, or the city government, apprise them of the pond situation, and then go to work by a different route, avoiding the pond henceforth.
The analogy should be clear. There are children whom I can save by donating large sums of money per child to get them mosquito nets? Why am I on the hook for this? This will never end. Are there not more systematic ways of dealing with the whole situation? Some sort of mosquito-net mass production program? Eradicate the mosquitoes somehow? Stop having children?
To view it from another perspective: one of the reasons I would save the drowning kid from the pond is that I want to live in a world where if something bad happens to someone, like "oh no, I am drowning in a pond", nearby people who are able to help, do so, even at some (not entirely unreasonable) one-time expense. However, I don't want to live in a world where bad things happening to people is just a fact of life, and other people end up having to reduce themselves to pauper status to continually fix the bad things.
Saving the child is a causal step toward the former world. Donating to AMF seems to be a causal step toward the latter world. Show me a way to fix the problem forever, and I might be interested. "Eradicate all the mosquitoes" seems like a possibility (we did it here in the U.S.). "Stop having children" might be another (though I'm not sure what would be the best way to accomplish that).