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?

There's something to these concerns (see the first and third bullet points here), but I believe that the broad picture is that if donors to AMF didn't step in then the children wouldn't be covered by mosquito nets. That said, I think that your concerns do reduce AMF's expected value somewhat.