Indeed, calling it just "riding" is one of many odd horsepeople shibboleths. This is actually my other huge nerd topic.
Other ones include that nobody calls them stables, it's "the barn," there is a difference between a rider, an owner, horsewoman, horseman (horseman is a reverently reserved term of respect, and horsewoman is also a term of respect, both take a few decades of riding to earn, when a horsewoman is a horseman, it's like saying Maestro, it's deference). English and Western riding are a level of detail equivalent to red and white wine, they sort of describe more what you don't do more than what you in fact do. A trail ride is called going out for a hack, or going hacking, and a horse that is safe on a trail is called a good hack. Disciplines are very siloed and the equivalent difference would be someone interested in rally car racing vs. street racing, where they both like cars, but wouldn't have much to talk about other than some technical rivalry. It's almost to the level of the difference between SWE and devops, you're both "good at computers," but that's about all they have in common.
Wrt motorcycles, we also say motorcyclist or biker, not rider. Funny that the differences between motorcyclists and bikers are alot like that of English and Western riding, as they're motivated by different things.
Also, I've eaten a horse steak. I don't crave it, but it's neutral. Part of our human stewardship of nature involves killing, culling and eating other animals, just as bugs will devour my body once I go. The squeamishness around eating horse meat seems more like a fear of ones own mortality after being confronted with the body of a being one empathizes with. It's a free preference and choice, and I would only say that fear is expressed by people who would judge others for eating the meat, but not by someone who just doesn't eat it.
source: rides motorycle to the barn to go on a hack to unwind after hacking all day as a desk jockey and using hack writer skills to comment on hacker news.