Its not like language is some natural kind term that we figure out the definition of via investigation... language just is what linguists say it is.
What you are doing is like going on a baseball forum and saying football is baseball, citing various things to support your claims (they both use a ball! they both have points! they both have teams! etc. etc.) but not realizing it isn't up to you... its not a matter of investigation or debate. Baseball is just baseball, and language is just language. If linguists say that language requires x, y, and z, then it does. There has to be a dividing line somewhere between language and non-language, and the people who decide what it is are linguists, not laypeople. They choose the line not for some grand reason, but just because defining languages as they do brackets them off for study in a useful way.