Why does the difficulty of Go depend on a rule about repeating positions?

Because the rule decides whether a game of Go can go in circles. Computer scientists sort problems into complexity classes by how much time or memory they need as they grow. EXPTIME, for example, holds the problems a computer can solve in exponential time, and PSPACE those it can solve with a polynomial amount of memory. Imagine Go played on boards of any size: how hard it is to decide who wins a position depends crucially on the ko rule. With Japanese ko rules, which forbid only the basic ko (a move that reverts the board to the position one move earlier), Go is EXPTIME-complete. With superko, which forbids repeating any earlier position and is used in most Chinese and US rulesets, it is an open problem what the complexity class of Go is.

The tiny rule matters because Go is almost in PSPACE: in normal play moves are not reversible, and only captures allow the repeating patterns that would make it harder. Japanese rules allow longer repeating cycles, such as the triple ko that allows a cycle of 12 moves, and so a game could loop forever. Superko is subtler: Robson, who proved the Japanese-rules result, showed that in some games the superko rule means even finding the legal moves can require exponential space, because the history leading up to a position can be exponentially long. For Go under superko, both bounds of his proof break.

The scale of Go was noticed long before computers. In the 11th century the Chinese scholar Shen Kuo estimated in his Dream Pool Essays that there are around 10^172 possible board positions. More recently John Conway's research on Go led to the surreal numbers. The point of all this is that "how hard is Go?" has no single answer: it depends on exactly which rules you play by.