I don't buy that. If we use the example of height alone, the vast majority of women would not date a man shorter than them regardless of whether the man has a "likable personality". https://www.youtube.com/watch?v=ZbG05ePWRQE
So do you now agree this statement is obviously false?
Height is just one of the first filters women use, and often the requirement is more strict than just "taller than me". You also have to pass other commons filters. Another very important filter for most women is race, and we're just getting started.