Unless I missed something, the "completely reasonable reason" appears to be that horses live a lot longer than dogs.
Really, once you learn that there people who could reasonably prefer mini-horses to dogs, the article has answered the question it sets out to.
I have a very hard time believing that. Do you have a source? It's all anecdotal, but the few people I know with dog allergies, seem to be very mild cases. While horse allergies seem to be fairly common and much more severe.