Why do we draw?
Here is a first list of reasons for drawing:

• To observe
• To record some real phenomenon, such as a scene or a person’s face
• To play
• To explore, to follow a line
• To think
• To capture some essence of an object being drawn
• To become one with the object being drawn
• To communicate something, for example, an emotion, a mental state, an idea, a thought, an inference, . . .
• To express some prior internal emotion or mental state
• To express some internal emotion or mental state concurrent with drawing, something that arises in the act of drawing
•  To invoke some emotion in the drawing
• To provoke some emotion or mental state in the viewer of the drawing
• To inspire viewers to action, as, for example, in political posters or satirical cartoons
•  To achieve some internal emotion or mental state by drawing –  for instance, to seek to become calm, to seek to enter a trance, to seek to be in the moment
• To better know oneself
• To seek mastery of the skills and arts of drawing, to train oneself in these arts, to undertake a practice (in the Zen sense of that word)
• To pray
• To communicate with non-material (spirit) realms
• To achieve or to progress towards religious salvation
• To provide soteriological guidance to others, as Shitao and his Buddhist contemporaries believed they were doing in China of the early Qing Dynasty (See:  Hay 2001).
• To pass the time.

More on drawing-as-thinking here.  For comparison, some reflections on the purposes of music here, and on music as thought here.
 
References:
Jonathan Hay [2001]: Shitao: Painting and Modernity in Early Qing China. New York: Cambridge University Press, Research Monograph Series.