In response to this argument, I have made a number of points. One is that the vocalizations and gestures used by many animals as a form of communication lack the characteristics of the words used in human language (see here). Another is that animals use signs to communicate, whereas human language employs symbols. To understand the distinction between these, please see my previous blogposts "Why Animals Don't Have Language: Two Arguments" and "'They Have Nothing To Say': David Berlinski on the Illusion of Animals Learning Human Language."
A recent blogpost at Mind Matters, entitled "Why Animals Don't Really Have Anything Much to Say" suggests three more reasons for being skeptical about the claim that animal communication is similar to human language. First, animals seem incapable of using human language except in a very limited way. This is illustrated by the case of Nim Chimpsky, a chimpanzee trained by animal behaviorist Herbert S. Terrace to use American Sign Language (ASL),. As the blogpost notes:
Terrace concluded that the only reason Nim (and other chimpanzees) signed [used ASL] was to obtain rewards. Were it not for the teacher, Nim would try to grab a reward directly. When that failed, Nim learned that he had to sign to obtain the reward. Anticipating Nim's signing, the teacher inadvertently made one or more appropriate signs, about a quarter of a second before [Nim] signed. Terrace also showed that prompting explained the signing of other chimpanzees who were trained to use ASL. Because Nim only signed to obtain rewards, his signing was limited to the imperative function of words [that is, commands or requests]. That differs fundamentally from [language's] declarative function, which is to name objects conversationally.
The fact that the use of ASL by Nim and other chimpanzees was limited to the use of imperative forms most likely was due to a fundamental difference between the nature of animal communication and the nature of human language. Animal communication appears to be essentially instrumental in nature. In contrast, while human language can be used instrumentally, it also can be used for a number of other purposes. Moreover, this inability of animals to use human linguistic forms other than imperatives is bad news for any theory that postulates that human language evolved from animal communication. This is because, as Mind Matters points out: "Imperatives are a miniscule portion of human vocabulary. If human communication were limited to imperatives, language would have never evolved."
A second reason for skepticism about the alleged similarity between animal communication and human language is that animal communication, unlike human language, is not used to engage in conversation. As Terrace himself noted in a blogpost for Psychology Today:
Animal signals, which are typically uni-directional, are never part of a conversation. A vervet monkey that sounds an alarm for a leopard doesn't expect another monkey to say, thanks, I've already seen it, glad you told me, and so on. In those rare instances in which one animal answers another animal's signal, as for example in bird duets, the answer is innate and immutable. It never adds new information.
A third and final reason for doubting that animal communication and human language are essentially the same is that the number of signals used in animal communication is dramatically smaller than the number of words contained in human languages. Again, quoting Terrace from the same blogpost:
...there is no limit to the number of words a person can learn. It has been estimated that college students [know] more than 40,000 words. So long as there are new objects or actions to name, people can increase their vocabulary, for example, with the names of new elements, stars, diseases, countries, and so on. [Conversely, because] animal communication is entirely emotional, the number of signals an animal can make is limited, rarely more than a dozen in a particular species.
To conclude, there are numerous reasons to reject the idea that animal communication is basically the same as human language. To the extent this is true, it becomes all the harder to explain how human language could have evolved from some form of animal communication. Consequently, I would argue that it is more reasonable to believe that the human capacity for language is a gift of the Creator, not the result of a blind process of evolution.
Photograph of chimpanzee by Chi King, from Wikimedia Commons