What is the cause of logic?

Need or desire to sort beans, determine land borders, etc., and, as doing such things became more intricate or complex, the desire or need for quality assurance in the sortting, measuring, etc. of that process.

When Godel proved that logics are self-incomplete, von Neumann noted that an incomplete logic may, with placement into a further logic that develops as a matrix "enveloping (axiomizing)" the first logic, be "completed" within the second logical framework. 

An enquiring mind capable of self-awareness.

The "cause" is our human capacity for memory; identifying, analyzing, and comparing phenomena; recognizing patterns and trends; employing both inductive and deductive reasoning; and then testing the conclusion through further experience and evaluation.  Some are better at it than others.