How's “drag” (tractāre) semantically related to “handle, deal with, discuss”?
How exactly did tractāre branch out "metaphorically to ‘handle, deal with, discuss’"?
How does "dragging" semantically appertain to ‘handle, deal with, discuss’?
Dragging connotes physical effort, e.g. if a human or animal is dragging objects behind them. "Deal with" and "discuss" feel more like business or transactions to me, and business and transactions don't usually require you to drag objects!
Treat comes ultimately from Latin tractāre, a derivative of tractus (source of English contract, tractor, etc), the past participle of trahere ‘pull’. Originally tractāre meant ‘drag’, but it branched out metaphorically to ‘handle, deal with, discuss’, and it was in these senses that it reached English via Anglo-Norman treter. The notion of ‘dealing with something by discussion’ also underlies treatise  and treaty , which come from the same ultimate source.
Word Origins (2005 2e) by John Ayto. p 516 Left column.