For a lefty, you're correct. But for a righty, then the right hand would be south. So, that can't possibly be the reason why boxers call lefties 'Southpaws'
The parent comment makes perfect sense to me: a left-handed person would have their left hand south. So their main hand is the south paw.
Your parent comment points out that for a right-handed person, their right hand would be south. The same is true for either handedness, thus does little to differentiate the two.
Left handed fighters put their right hand south. Their left hand (jab hand) closely guards their cheek/chin. So it can't possibly be south.