I reckon: some shepherd, WAAAAY back when, came up with it ... I can't speak for any of the other possible origins/histories, but I learned pole/staff by way of Wu Shu ( Kung Fu ). I spin a six foot pole, (not like the short poles I see other twirlers use), largely; modified combat moves, a la the Shaolin Temple and Jackie Chan.
The Shaolin Temple really took off around 520 AD, I can't say for sure when the pole was formaly studied and developed as a weapon. The pole/staff is reportedly one of the favoured 'weapons' of the Shoalin Monks ( Movie Reference: The Shaolin Temple, starring Jet Li ).
As a combat style there is very little 'throwing' of the pole. If at all, the pole is thrown in such a way that it momentarily distracts the attacker, while the thrower moves in, grabs the pole, and then, er, crunches the attacker ...
My pals learned staff from 'Hippies who'd been to India' and their style is radically different to mine. Lots of throwing, lots of fast, frenetic sequences. A six foot pole is slow by any stadards (thus ideal for meths+boric acid), but far more mesmerizing than poi and therefore ( 3 dots ), IMHO, a pole is more suited to someone who dances WHILE they spin ...
In a nut shell:
The History of Staff = History of Entertainment. Some one did it, some one loved it. Don't stop ...