It’s obviously passed down through tradition. It might not be written down per se as an official rubric, but by using tradition, common sense, and biblical references, we can see why we cross ourselves with our right hand, rather than the left. We do not bless ourselves with the left hand. Priests don’t bless with their left hands, nor do they incense with their left hand. When they wear a maniple, they wear it on their left arm, which understanding what the maniple symbolizes, only strengthens why we cross ourselves with the right hand.
I’m a very left-handed person, but even I can see why and understand why we cross ourselves with our right hand rather than the left. I don’t need to break tradition in an “I’m left-handed, so I’m gonna be stubborn and use my left hand to make the sign of the cross because nothing is written down that I don’t have to” protest.
When you go to make the sign of peace in Mass, do you stick out your left hand too? You know, there’s nothing saying you must use your right hand to shake the other person’s hand.