Men are getting those ideas from other men who are in a cultish group though. It's wildly skewed.
For example, it may be true that we have a mild preference for tall men. But, "tall men" means taller than her, not 6 feet. See how that gets warped and changes things? If she's 5'2" and has a mild preference for "tall", any guy who's 5'3" will fit the bill.
The biggest thing here is that the behavior of short men often exclude them. Many have little big man syndrome because they've been mocked and bullied in youth and never got over it. This is not a fun personality to date. So he might get rejected based on his height, but his height is only secondarily related to the rejection. In other words, he got rejected befause of how he feels about and behaves in relstion to his height, not directky because of his height.
There are also tall women who prefer shorter men. There are also short women who prefer a huge height gap. I can understand this too, because in a crowd, a tall man can clear a path. Short women get bullied too, constantly teased, and often manhandled in adulthood. You're more likely to have men cop a feel if you're small. Being with a really big guy is freeing in a way to small women.
I think I thought, that most people prefer a near height pairing, with both men and women preferring the man to be slightly taller, no more than 3 inches. When you look at pairings in public, that's what you mostly see, regardless of what gets reported in surveys which are often asked in ways that will lead to inauthentic answers and results.