There are always outliers. There are also men who like overweight woman. BUT: Genes hold culture on a very very tight leash. But even if it would be nurture. This is not gonna change anything for the individual person affected. It it not changing in his lifetime.
http://www.sciencedirect.com/science/article/pii/S019188691530060X
Correlation and Causation.
This might be true, but it might also be affected by the better social status of taller people, as said before in this thread. Taller guys get better jobs. Or it might be one of numerous other factors playing into this.
I myself am 5'7 and never really had problems dating since I have a very nice physique and the corresponding confidence.
It's a problem with stuff like Tinder though. Height creates a bottle neck at the beginning of the conversaion or even before a match that doesn't even give you the chance to play your cards right.
I've had taller girls, but my girlfriend is smaller than me and i couldn't be happier. She never even mentioned height.