The way I rationalise it is this: Most of us are right-handed. Of the two main hand operations in driving (gear changing and steering) steering is the most crucial to safety. So, when changin gear, we want the "best" hand on the wheel and the "worst" one fumbling with the gear stick. I think this is an excellent reason, (and maybe goes some way to explaining why manual shift is so little-used in the US??)
I once heard (don; know if this is true) that we have "eyedness" as well as "handedness" and that, as with hands, the right is usually dominant. Hence, overtaking would be safer for drivers here than in, say, France, as our right eye has a slightly better view before pulling out. As I say, I don't know whether the eye thing is true, but if it is, that's pretty good reason.