As we learn more about critters we are finding far more variability as well as far more commonality than we supposed. Dialects between bird populations varies geographically as well as over time. The same is true for ground squirrels and prairie dogs. Whales have dialects that extend down to the individual level as do elephants.
So what we see in other critters is very much the same as what we see in human populations. We find similar stories around the world because there are similar conditions and events. There were floods and landslides and storms and lightning and fires and wars and love triangles and dominate parents and unruly children and leaders and failures and crooks and heros and gain and loss.
Why wouldn't language, like writing, like astronomy, like art, like agriculture, like so many things, be an example of repeated, independant discovery?
That may or may not be true, but the other similar characteristic I'd point to would be innate curiosity. Wouldn't that make multiple independant language invention events even more likely?