It's funny when girls say they don't date short or Asian men because, "it reminds them of their family." That's mere rationalization, because the truth is painful or uncomfortable.
Short women from tall families want tall men, because
they come from tall families. Short women from short families want tall
men, because they don't want their children to be short (or they'll say they didn't get along with their family). Replace short/tall with Asian/White and you'll get the same story.
It's all just a mental lie that people create so they don't have to
think, "I've been taught that taller/White men are better than shorter/Asian men, and
so that's why I want to marry a tall White guy."
When you discount millions of people, based on a genetic trait they have no control over, you're shallow whether you make excuses or not. Simply own up to it: you care what society thinks of you. The rationalizing just makes you even scummier, and you're not fooling anyone intelligent.