Getting someone's goat (To upset them)
An age-old tradition was to keep a goat in a stable with a racehorse to act as a sort of calming companion on the night before the race itself.
However, if a rival wished to sabotage the impending race, they would go and steal the goat from the stable which would upset the racehorse and throw their game off on the next day. Therefore, it is a deceptive way of sabotaging or enraging a situation.