Why is there usually a plastic coating around a metal wire?

There are a number of reasons:

If the wire is electrical then it is covered in plastic as plastic provides insulation, this means that if adjoining wires come into contact the electrical current would not cause a short circuit. Normally electrical wire is cooper as it is a good conductor of electricity and does not oxidize/ rust easily.

Secondly wire hangers are covered in plastic to prevent the metal (normally mild steel) from rusting. If they were to rust, it would cause orange/ red stains on your clothes.