The problem Swift is addressing is the treatment of the poor in Ireland by the wealthy. He proposes a ridiculous and disgusting solution to the population growth of the poor in the hopes that it will force people to see the truth. The poor were being treated with cruelty and indifference. Swift forces the wealthy to see them as people by suggesting they eat the children.
Swift is also expressing his frustration with solutions to current problems that he considered just as ludicrous. In way, he was pointing out how ridiculous some of the actual proposals of the time were by showcasing a ludicrous solution of his own in the same manner.