The very process of learning would support your statement. Children can speak in quite mature ways before they can ever begin to write that way. As a matter of fact they can also read quite sophisiticated texts before they can write in any sort of mature way about those texts, much less write in a way that mimics that text.
Since the ultimate goal of a language--the word derives from the Latin word that means tongue--is communication, it is only logical that language begins with speech, which is a single function rather than the more complex one of writing which requires the additional acquistion of symbols for the spoken word.
This makes sense on the face of it because speech certainly came before writing in terms of the development of writing. Languages developed orally and then writing appeared and was used to record what was already happening in terms of speech.
Of course, modern languages are as much written as they are spoken. For that reason, this is a problematic idea. It seems that written language is at least as important as spoken.
This link gives you a great deal of discussion of the scope of linguistics: