The basic argument for the innateness of language is poverty of stimulus. This contends that our general human intelligence and the samples of a given language fed to us in the first five or so years of life just aren't good enough to produce the linguistic competence of your average five-year-old. In order to understand the input, the infant must have some tendency to look for the kinds of patterns that appear in language, at the very least.

A five-year-old's command of language, if it's just another complex, patterned input for babies and small children to take on board, is a pretty good trick. As unlikely as a child playing Handel's Messiah on the piano after hearing a couple of CDs of unrelated music. And this is almost every child, whatever their level of general intelligence. Put like that, the mysterious language instinct is the least unlikely explanation.