What about 'sign language', music, morse code, mime, and mathematics? What about the barking of dogs, the songs of birds and whales and dolphins, the scent trails of ants, the dance of the bees? Computer programming languages? Computer machine code? Which is a language and which is not?
Language is that which helps language-users 'manage' or 'deal with' information. Language is that which helps language users create, locate, capture, transmit, or receive information, as a first step on the road to truth or meaning. (There may not yet be computers that meet the conditions of 'personhood'. But there absolutely are computers who are language-users. In fact, all computers are language users.)
Note that in the previous paragraph, instead of the phrase "that which helps" I could have written "a process in which", or "a mechanism whereby" , or "a framework upon which" or "a domain where" . The point of listing these metaphorical phrases is to highlight that Language has no intrinsic, absolute meaning. People select words to speak or write on the basis of closest fit---not best or perfect fit---to the true and real meaning that exists outside of the approximation called Language.
There is no ultimate proof of the extent to which language truly and accurately reflects what is in the mind of the language user when ze uses language. As with Arithmetic, language is another formal system in which Gödel's Incompleteness Theorems apply.
As Humpty Dumpty remarks, in Lewis Carrol's "Through the Looking Glass, "When I use a word, it means just what I choose it to mean –- neither more nor less." Every day, billions of people do the same as Humpty: use language to create individual, idiosyncratically personalised relative meanings. They do so because it is simply not possible to create absolute meaning via language.
Frequently the distinction is made between "literal" and "figurative" meaning. It is startling to realise that in fact there are no literal meanings at all in language---zero, zip, nada, nothing. Language is an approximation: all meanings are figurative, to a greater or lesser degree. Language is a metaphor made up of sub-metaphors, sub-sub-metaphors, sub-sub-sub-metaphors, etc.
The absence of absolute truth in language means there are no real, absolute, substantive disagreements or arguments between language-users; there are only insubstantial and relatively unimportant differences about the application of labels (words)--(what I call the illusion of difference.
Language is the domain where meaning is created, captured, transmitted or received. Thought is another such domain. And as well as Language and Thought, there are other places where meaning resides. Thought without Language---without Words---is possible, though difficult to achieve.