Strange that this article doesn't mention any of the current research into what the cause is. [Erich Jarvis](https://en.m.wikipedia.org/wiki/Erich_Jarvis) has done research into the neurological mechanisms and seems to have discovered that animals capable of complex speech patterns have some mutations that permit a neural connection to grow from the motor cortex to the larynx (or syrinx in birds) by way of the brain stem. In other words, we can make complex vocalizations in part because we have fine motor control over our voice box, whereas most other animals do not.
This is only part of the story — there's still the question of how auditory information makes it in as an input so that we can replicate sounds we've heard — but it's a pretty big part for TFA to omit.