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 : 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.