I have read plenty regarding the debate on what direction and angle the mezuzah should be mounted. That said, I have never heard a clear explanation as to why we always mount them on the right side of the door frame.
Even in the Shema the text does not explicitly state "upper right quadrant of the door frame" when directing us. It simply states door frames in a general sense.
Do any of the sages give us clarity on why mezuzot were standardized to the right side? Is it something we have a clear answer for or is it simply the way it has been done so we don't question it?