I have heard the same thing. I was told it was so if a car passed by and splashed water, the man would shield the woman from getting wet. I always walk between the road and my wife. Just habit I guess. And yes, I was raised in the south.
My wife explained it to me as I'd be the one hit by a car if one jumped the curb, lol. I told her that if a car is coming at me, I'm getting the hell out of the way and she should too.