So I think I've figured out why women are so disgusted to hear someone call them fat or overweight, and similarly why they think nothing of dismissing short guys. So:

When you call someone (especially women) fat, you're implying an array of connotations. Calling someone fat implies that they are lazy, unmotivated, unattractive, unwilling to change, etc. Obviously these would be undesirable qualities regardless of gender. We already know that women are the indirect communicators of the 2 sexes, therefore they are the ones who seek hidden meaning between words hence all the things they assume you're also saying about them when you call a woman fat.

The reason they can dismiss short men is because there is no connotation to calling a man short. There are no personality traits you can assume from a short person like you could an overweight person. Thus, to them there is no character attack from labeling men short so they're fine with sticking a height requirement to all the men entering their bedrooms.

TLDR; It's not calling a woman fat, it's calling a woman a fat person and all the things associated with being fat.