I think I should clarify this considering how pervasive the claim is. The claim “DNA is a language” is probably the result of pop-science, which tries to reduce concepts to simple single words or phrases. That’s how the myth “you only use ten percent of your brain” started (Complete nonsense. The confusion arises because only 10% of brain cells are neuronal, the rest are glial cells like oligodendrocytes and astrocytes). It is also how the Second Law of thermodynamics became reduced to “everything progresses towards disorder” with the result that many creationists are confused about thermodynamics, and labour under the delusion that entropy can never decrease in a system. Nonsense, again. But it does reveal troubling ignorance about science, a few names, some general concepts, that’s it. The claim “DNA is a language” is a meaningless allusion, even if construed as metaphorical. DNA is no more a language than a telephone book is a computer. DNA is a cipher, that is to say that it is a direct substitution representation of the sequential structure of another unbranched polymer, polypeptide (some DNA, however, codes for RNA genes), constructed of a different monomer class, amino acids. The order of the amino acids will determine the structure and function of the final product for which the DNA codes, the protein. In this regard, DNA does not function, even analogously, as a language, it is a substitution cipher. A substitution cipher is one in which one set of functional expressions is replaced with another. For example:

A=1

B=2

C=3

D=4

E=5

F=6

Etc

If I transcribed this to write: 85(12)(12)(15)=HELLO, which was then decoded by another conscious being with the same understanding, then it would become a language. This does not analogously occur in DNA. The DNA is a substitution of DNA bases grouped in to codon triplets, which are transcribed and translated to make functional polypeptides. This is not a language. A substitution cipher per se does not qualify as a language.

In this case, each amino acid is read as a triplet group of nucleotides called a codon, with other codons dictating the stop and start of translation. As shown in this table, DNA is a substitution cipher like so:

However, DNA is not a language, in any sense, because it does not represent concepts or meanings, a language entails that abstracts represent concretes, such as a number 5 written on a piece of paper, which has “meaning” to an entity which can understand what “5” means. Nothing analogous is found in DNA, since it is only a substitution cipher, which represents the order of amino acids in a protein, or RNA nucleotides in an RNA molecule. There is no abstract representation or assigned meaning going on with a direct physical substitution cipher, like DNA. When a stop codon orders a ribosome to stop transcribing, the ribosome does not “understand” that it has to stop transcribing, because it is just a ribosome. Nor does the nascent polypeptide “understand” that it is being hydrolyzed. Nor do tRNA “understand” that they must bind to their respective codons on mRNA. There is no transmission of conscious understanding, no abstract communication that entails one entity interprets symbols because it has the same understanding as the entity which communicated them. In this regard, DNA is not a language by definition. All that is happening is that the stop codon does not contain the binding site for any tRNA, but it does contain the binding site for the release factors which terminates translation because it causes the nascent polypeptide to hydrolyze an ester bond as they catalyze this hydrolysis reaction and release from the subunits of the ribosome.