Most men would say they prefer a short woman based on his experience. Even if a man wants to experience to date a variety of tall women, there just aren't as many tall women out there. Most men date shorter women.
It's easier to find a match when a man is taller and a woman is shorter just because most women prefer tall men.
Most women prefer taller men. Men aren's as string about height requirements to women only because men's self worth often comes from money and status rather than his looks. In a woman's world, a woman is judge by looks a lot more comparing to any man, this is why no woman really wants to feel oversized and too masculine. Women are a lot more picky about height than men are, this is why it give men such a small choice in a dating pool.
Preference is preference but what really do men and women want? Women want attraction and chemistry. When women say they love men for their personality, it means that women often have no clue why they get attracted to someone, they just feel attraction and they love it.
If a woman is sexually attracted to a man, he will make her happy even if he is much shorter. Women want to feel good.
But attraction isn't everything that men or women want. Other qualities, as social status, money, kindness, good habits, generosity and many other qualities are very important. Women and men don't just base their choice only on height or only on money, they take a total package, what they need the most and then they realize whether the are in love or not, whether they really want to be with someone or not.
So many men worry about height, about money, or looks, but what women are looking for is a total package. Men are the same, they want a woman who could be a total package to make him happy. In my opinion, men generally have less requirements to a partner comparing to women. Women are a lot choosier and harsher in what they want and their personal requirements. Men mostly want a beautiful sexy woman and women want so much more than that in a man.
If you are a man or woman, don't worry too much about one physical quality but worry more about the total package, worry about what both of you want and what both of you can offer each other to be happy.