To refute Saussure's claim that the relationship between signified and signifier is arbitrary, one might be tempted to point to the phenomen of onomatopoeia--the use of words whose sounds somehow evoke the concept to which they refer, like meow, used to express the sound a cat makes. There are, however, two problems with this counter-argument. First, while onomatopoeia does exist in many languages, the number of onomatopoeic words in any language tends to be relatively small. Second, even onomatopoeic words often differ from language to language. For example, the sound a rooster makes is cock-a-doodle-do in English, but in French a rooster says cocorico. In other words, even onomatopoeic words are somewhat arbitrary, as they depend on the particular language. As for written language (whose development postdates spoken language), while the written symbols in a so-called ideographic system like Chinese sometimes do suggest graphically the concept signified, the majority of these symbols are not purely pictoral in nature.
If, then, the signs that make up human language--often called lingustic symbols--are arbitrary in nature, then how are human beings able to use them to communicate? The answer is that linguistic symbols work because of agreement among the users of a language. As Jeff Roesler Stebbins says in his article "The Evolution of Evolutionary Linguistics" (Colorado Research in Linguistics, June 2007): "[Linguistic] symbols are triadic conventions involving the speaker, the hearer, and a referent [concept]; because they are arbitrary, they work only if agreed upon by those who employ them. Agreement entails a theory of mind [the idea that other consciousnesses exist], of course, and must apparently be reached through the use of language (i.e., other symbols)." In other words, in order for there to be agreement among language users as to the meaning of a particular word, they must use language (i.e., other words) to achieve such agreement.
I don't believe it takes much thought to realize that this apparent truth about the nature of language creates a problem for any theory explaining the origin of human language through an evolutionary process. If human language can only develop through agreement among its users as to the meaning of words by means of language itself, then how could language have developed in the first place? There is, in effect, a sort of "chicken-or-the-egg" dilemma. I suppose one could argue that initially human language was onomatopoeic in nature, but that assumes that each everyone would have, for example, perceived (auditorily) the crow of a rooster in the same way--which, as my previous examples from English and French suggest, might not have been the case. More importantly, at some point creating words through onomatopoeia would have reached its limits (for example, it is difficult to see how there could be an onomatopeic word for an abstract concept like "good" !).
In short, if Saussure's claim that language is fundamentally arbitrary in nature is correct, then it becomes difficult to explain how human language could have evolved in a Darwinian sense. On the other hand, if language is something that was bestowed on humans by a Creator, as something that existed in the human mind from the beginning, then there is no "chicken-or-the-egg" problem. Thus, it would seem that evolutionary linguists have some explaining to do…