Question

Why carbon fibre is a non metal although having the property of ductility

Answer 1

Carbon fibre can be called a wire of carbon, but as carbon itself is classified as a nonmetal, hence carbon fibre is also a nonmetal.

Also, merely possession of any one property, does not satisfy the criteria for a material to be called a metal. other properties like conductivity, luster position in periodic table etc. also have to be considered.