This question makes the tacit assumption that when something exists, it must exist objectively. While I personally disbelieve the existence of a subject/object boundary, I can see why language elicits such questions. For example, languages must be learned, and hence obviously exists independent upon our perception. However, language is also defined by usage, hence its subjective nature.
Linguists will argue that there is no such thing as "proper English" due to any language's divergent and usage-dependent nature. A computer's "language" is a set of symbolic syntax in which the combination of small bits of information yield even greater amounts of information when the order itself is processed. Such "languages" are objective and universal (changes occur discretely in version numbers). Human language is similar, but new, slightly different versions are created with each speaker, and uniformity is heavily dependent upon human-human interaction.
(Consider Papua New Guinea, perhaps the most geologically diverse region on Earth. A good day's hike by experienced explorers yields only 3 miles. Most New Guineans have never been more than 10 miles from home in their lifetimes. Of the 6000 languages on Earth, Papua New Guinea is home to 1000 of them.)
Of course, if you want to go the more philosophical route, one may wonder if intangible information like language really exists objectively. I'm in the camp of most analytical philosophers in that simple (atomic) facts yield more complex information via their interactions. For example, the position of two objects is a simple fact, and the distance between the two is a complex one. Take this to the extreme, and you have the existence of extremely complex entities such as language.
Lastly, the role of language is to give a picture of reality, factual or not. Ideally, sentences could boil down to mathematical statements. Unfortunately, the actual usage of language runs more along the lines of "word games" in which ideas are inferred by creative juxtopositions of words (see: Wittgenstein's Philosophical Inquiries). Therefore the logic represented by "language math" can be true, false, paradoxical, contradictory, or nonsense. Most philosophical problems arise from the misuse of language.
I suppose that language acts as a mediator between reality and ideas, the subject and the object. A direct brain-to-brain connection would relay only ideas/feelings, whereas a rigorous mathematical language would be like a computer's language, relaying only previously defined consistent truths.