Not sure about biology, but it's certainly ingrained culturally. As a man, I'm constantly trained by the society to overcome rejection, and a typical dating pattern of men approaching women is a major part of this.
However, I wouldn't use words like "patriarchy" here because I honestly think that this assymetry hurts both genders equally, just in different ways.
Men have the disadvantage (or advantage) of facing rejection much more often than women. Whether men overcome the rejection and become more capable is debatable, although it's clear men are more accustomed to being rejected.
However, I wouldn't use words like "patriarchy" here because I honestly think that this assymetry hurts both genders equally, just in different ways.