Why DO I like the gray days?

Normally when the day dawnS (wiht) WITH a big and (shine) SHINY sun (the) people say(s): (makes a nice day!) WHAT A NICE DAY! But I feel the (contrary) OPPOSITE, the days that dawn with a big and (shine)  SHINY sun are (monotone) MONOTONOUS (it is better the grays days) GREY DAYS ARE BETTER. (these that rain very hard, ) WHEN IT RAINS HARD and we can (listen) HEAR the drops fall and (dead) DIE (in) ON (the) our window.

shiny OR shining OR bright / brilliant
A good phrase for heay rain in CONVERSATION is 'it is raining cats and dogs' - but this would not be in keeping with the mood of your text, which could be described as WISTFUL / CONTEMPLATIVE / MELANCHOLY  / POETIC / SAD

You should visit Scotland, well known as a land of rain and mist  Look at
http://tinyurl.com/2bqd5ae
and
http://tinyurl.com/25ugxp3

Why I like the gray days?

Normally when the day dawn wiht a big and shine sun the people says: makes a nice day! But I feel the contrary, the days that dawn with a big and shine sun are monotone it is better the grays days, these that rain very hard, and we can listen the drops fall and dead in the our window.