Why does interference only happen to monochromatic and coherent waves?

Answer 1

Think about it. Interference happens when crest and trough coincide to make black fringe and when crest and crest coincide to make white fringe.

If you have polychromatic waves, you will still get interferences but they will be hard to see because the fringes will happen a different intervals for each wavelength. So you will not see clearly defined black fringes.

And coherent waves are required because if you had light from all sorts of direction, then again interference would occur only in one direction and the potential black fringes would still get light from all the other directions.

Answer 2

Interference only takes place when the same wavelengths and frequencies of light come together.

That is why you cannot do experiments such as Newton's rings without a monochromatic source such as Cadmium or Sodium.