I agree, it’s a false division, or maybe more accurately an archaic and outdated one. Hunting and gathering is just part of being opportunistic feeders, and “Opportunistic Feeder” would be a great brand name for my next refrigerator. Toolmaking probably went from being for hunting or processing to being for self-defense really rapidly, and agriculture / gardening is probably so old we’ll never find out just how old it is.
You might appreciate the site history chapter of our project as it contains a repeating excercise in making such inferences.