Why is my light switch wired this way
This needs to be looked at by an Electrician as it looks like Vulcanized Rubber wiring (VIR). 

This is a Fire Hazard !!!

Your house wiring insulation may be the cause of the light not working.

Vulcanized Rubber is what they used before the 60's to insulate house wiring and overtime  it can become brittle and break off leaving the wiring without  insulation. 

dangerous old wiring- "Avoiding the perils of age"