Why do humans have the ability to be conscious, and other animals don't? 

The question implies a difference between humans and animals. On a relative level, humans can think, write, speak, develop theories, organise societies, etc. However, to Consciousness, there is no such difference between humans and animals. There is no mechanism within a human being that allows humans to have the capacity of being aware of being aware.

What the separate mind calls ‘a human body/mind’ or an ‘animal body/mind’ is, to Consciousness, exactly the same. Indeed, we are aware of being human, rather than humans being aware of being aware. It is not human beings that become aware, it is Consciousness that is conscious of a so-called human form. Consciousness only ever experiences and knows itself, independent of the forms it takes. 

In reality, there are no separate humans and animals. These are perceptual forms, appearing in Awareness, and made of Awareness.