Since you won't take my word for it, and seem incapable of seeing that your schoolboy physics doesn't apply in the real world, trying reading the research by Raymond L. Lee, Jr. in his 1991 paper: “What are ‘all the colors of the rainbow’?”.

I'll quote one paragraph from the intro that supports everything I've been saying above:

Some 50 years ago, Humphreys pointedly noted that "the 'explanations' generally given of the rainbow [in textbooks] may well be said to explain beautifully that which does not occur, and to leave unexplained that which does.'

Many nontextbook factors that affect the color and luminance of the natural rainbow still go largely unconsidered.

These factors include:

1. the angular divergence and coherence of sunlight,
2. the optical path length of rain showers,
3. the spectrum of raindrop sizes,
4. aerosol scattering and absorption,
5. aerodynamic distortion of raindrops, and
6. illumination of the rainbow's background

To do full justice to the natural rainbow, we must do much more than uncritically apply a rainbow theory to monodisperse, spherical raindrops that are illuminated by perfectly collimated light and seen against a black background.