This distinction is really rather regrettable. The reason I say that is someone who is going to carry a weapon for self defense should be trained sufficiently to be able to handle and adequately operate the weapon with both hands. Permit me to give you an example.
Having lived in Davenport, Iowa and being exposed to the training of the Chiropractors at Palmer University of Chiropractic, I am aware the course of studies is such that the student doctors are trained, regardless of their dominant handedness, to develop the muscles on both sides of their bodies, they are trained to develop the speed necessary to deliver a “high velocity, short lever” thrust using either their right or their left hands. Why? Because people don’t just injure one side of their bodies. The fact is, the student doctors practice and practice and practice and are actually tested to be sure they are able to perform without injury to the patient or without denying the patient the benefit of an excellent adjustment. That is all done in order to improve the health of another human being.
In the carrying of a weapon, it is critical you do no more harm than is absolutely necessary to stop the threat; hence, you must be able to perform with both hands.
So the question really is not what hand you are but rather on which side of your body would you feel most confident having the weapon reside when it is not in use and from which you could most easily deploy it in the event you are forced to do so.