Apparently, hiccuping is a throwback to a part of our evolutionary history where our distance ancestors still had gills.
I also like the way the author of the piece claims that
There must, however, be a reason why hiccupping persists 370 million years after animals started hauling themselves onto the land.
Apparently he or she is a subscriber to the old chestnut that there must be a reason for everything. For what it’s worth, I suspect that there is no good reason for the persistence of the hiccup—but since there is no obvious evolutionary disadvantage to keeping it, there doesn’t actually need to be.