Honestly it's not that girls hate short guys because of our height, it's the personality that come with it.
I'm 5'4 and so many of them have told me that many short guys are angry and have traits that most women dislike. I just try to act like any other guy, literally not even caring about how tall I am, and while it is a hardship in some things, it's just what I have to roll with.
I think it might have some basis, but taller usually means better genes and wealth (or it did centuries ago). It does make sense that women find taller men more attractive, but so does driving an expensive car or flashing an iPhone 7.
Also, I laughed hard at the Manlet Fashion meme, it's so hard to find shirts that fit my torso. At least I avoid cuffing my jeans, the fuck my shit up hairstyle and wearing shoes that make me look taller.