Because it's the one specified in the example? And you saying that this sentence is racist, due to the fact that it's stated that the dog is white, then that must mean YOU value black people over white ones, making YOU the racist. Racism doesn't just involve black people, you know. Jews, Asians, Arabs, and, yes, even white people get affected. Grow up!
Because in Italian the possesive pronoun comes with a definite article (with the exception of close family members) and in English it always replaces the article. You can't always translate word by word, different languages have different grammatical rules and sentence structure.
"Il mio cane è verde." (My dog is green.)
"La mia scarpa è verde." (My shoe is green.)
Verde doesn't change in the singular.
"I miei cani sono verdi." (My dogs are green.)
"Le mie scarpe sono verdi." (My shoes are green.)
The -e changes to an -i in the plural for both masculine and feminine forms.