First and foremost, not all Asian have small eyes. Mainly East Asians have small eyes, which does include China, Japan, Vietnam and Korea. Technically, their eyes are not smaller either, it just appear that way. The small, almond-shaped eyes came from what is called an epicanthal fold, an extra patch of skin of the upper eyelid that covers the inner corner of the eye. It is primarily an adaptive trait that helps to block some sunlight that reflects off the surface of snow. It’s the same reason we instinctively squint when we look at something that is too bright, to protect our eyes from what might potentially damage them.
In fact, these epicanthal folds could often be seen in young children of any race, and would slowly go away as they grow up for the non-Eastern Asians. Other races such as the San people, too, share these genetics advantage, in this case, to help block the glare of the sun from the deserts and Savannah. The eyes of the Asians get “rounder” the farther south in Eastern Asia, as the climate gets warmer. So in conclusion to your question of why do Asians have small eyes, the small eyes of the Asian are a defensive mechanism against the environment, all in order to protect our most precious sense, the sight.