According to the rules on measuring diagonals in the Pathfinder SRD:
When measuring distance, the first diagonal counts as 1 square, the second counts as 2 squares, the third counts as 1, the fourth as 2, and so on.
A medium character with a reach weapon threatens 2 squares away (10 feet). The first diagonal is five feet, so my character does not threaten that square, but the second diagonal is 15 feet away, so I don't threaten that either.
Does this mean an opponent can step inside my reach without ever stepping in a square I threaten and thus never provoking an Attack of Opportunity just by walking down my diagonal line?
This feels like a serious design flaw, so I feel like I'm missing something.