The mí reading is the 'something got in my eye' sense: dust or sand blinding the eye for a moment. Taiwan pronounces this sense mǐ. For deliberately narrowing the eyes, the reading is mī.
目 on the left is an eye stood on its end, pupil framed by lid lines. It indexes 眯 in the eye family with 看 to look, 睡 to sleep, 瞎 blind, marking it as something the eyes do.
米 on the right supplies the sound with a tone shift, mǐ to mī. It also adds a faint image: a tiny grain is exactly the kind of speck that gets in an eye. Same phonetic appears in 迷 lost and 谜 riddle.
