Actually human languages are much better suited for all kinds of communication :
To the best of our knowledge, most animal systems of communication don't allow reference to either the speaker (i.e "I"), the hearer (i.e "you"), or a distant third party (i.e "it"). Even elaborate systems like the bee dance are highly specialized in the type of reference that is possible.
In human speech it is possible to talk about things or people that are not here, things that don't exist but may, things that have existed, things that will exist, things that won't exist. Hypotheses, conjectures, and so on, are not part of any other species way of communicating, as far as I know.
Furthermore, all known human languages allow you to attribute utterances to another, earlier speaker, what is known as reported speech (often, though not always as Pirahâ demonstrate, through an embedded clause "He said that X").
Human non-verbal communication (which is EMPHATICALLY NOT to be confused with sign languages), on the other hand, is typically not very expressive. Apart from the admittedly very important, but nevertheless quite specialized domain of human emotion (conveyed by facial expression for instance), it is more or less inadequate for much of what we want to communicate.