If you are trying to win a debate on if equestrian pursuits is a sport, youd need to use adjectives and examples that are actually part of the definition of sport. Saying it hard, so is pushing a broken down car,
Saying it takes mental skill, So does calculus,
Saying you can get injured, So does construction work,
Saying you have to trust a large animal, so does a dairy farmer.
None of those help you. You need to focus on the definition of Sport.
Acording to Webster: SPORT noun
a source of diversion : recreation c (1) :
physical activity engaged in for pleasure (2) :
a particular activity (as an athletic game) so engaged in
Riding a horse clearly meets the English definition of sport.