Question: As light is electromagnetic radiation. Then why I don't see any magnet bending light wave? Or why light doesn't diffract whenever it passes by a live wire?

Answer: 
In vacuum electromagnetic fields obey superposition to a very high degree of accuracy. A magnetic field does not have any effect on light. Light in material media *can* be affected by a magnetic field. This is known as the [Kerr effect](https://en.wikipedia.org/wiki/Kerr_effect).

As for current carrying wires, these reflect and diffract electromagnetic waves like any metallic or dielectric object. This is why you see them. However, there is no effect of the current until the wire heats up.
Electromagnetic fields simply superpose. They don’t interact with each other. (I am ignoring quantum effects at *enormous* field strengths.) Two waves go right through each other. A wave goes right through a static field.

Electromagnetic fields interact with *charges*. No charge, no interaction.