The main problem with the nativist hypothesis is that it's breaching Occam's razor rule. Is there a simpler explanation than being hardwired with information, which would be a fairly complicated thing to explain, considering what we know of the brain today? Yes, there is: languages are related and sound symbolism could be passed from language to language, or the perfectly reasonnable explanation offered by Christine Cuskley at the end of the article. In the world we live in, some set of sounds are associated to small animals, other to big animals.
Nativist hypothesizes suffer from a lack of imagination in looking for alternative explanations. I cannot explain it? Must be innate! Or, children do it? Must be innate!
Cognitive research points to a much more promising explanation: we are really good at learning, and we can learn abstract concepts pretty quickly, even as very young children. See Stanislas Dehaene's work for instance.
Abstracting concepts for big and small from our environment and associating sounds with it is much more plausible than passing around information about abstract concepts in genes through natural selection based on random genetic mutations.