Why do you think some women don’t like the idea of dating a man who is shorter than themself?

[Anonymous]

I am assuming these women feel the taller the man is the more physically strong they are so they feel more protected around a tall man.
Taller people have the ability to potentially carry more muscle since they have a larger body frame they can carry more muscle inside them.

[patrick994]

The evolutionary reasons why many women prefer taller men are mainly based on protection, status and genetic qualities. In the past, a taller and physically imposing man could offer greater security against predators and rivals, increasing the chances of survival for the woman and her children. Furthermore, height is often associated with dominance and social success, which meant better access to resources and a greater ability to take care of the family. Finally, greater stature may indicate good health and a strong immune system, advantageous characteristics in partner selection. These evolutionary factors, however, are now mixed with cultural and personal influences that can alter individual preferences.

[OneViewpoint]

A man = status for a woman. He's an accoutrement, a fashion accessory. Women compete for taller men and taller men are in relatively short supply. Hence the perception of value due to scarcity exists.

There is also the biological drive for women to choose an able "protector", and taller larger men are perceived to be more capable of providing protection. Women like to feel safe.

[Berethor]

Men are 5 inches taller than women on average, so shortness is a feminine trait.

[Anonymous]

For the same reason some men typically do not want to date women FATTER than themselves.