Right off the bat, I have to deal with two issues: First, that kid is too old to have her father in the dental office with her at all. The doctor's "what's with your dad?" probably didn't mean "why is your dad riding a horse" but rather "why is your dad in here instead of the waiting room? Are you the biggest five year old on the planet, or are the apron strings really that strong in your family?"
Second, one of the comments under this video reads "I don't think they should have squeezed a horse into a small space like that." Which leaves me very, very concerned that the guy who left that post believes that this is an actual dental office and not a prop-filled sound stage. Maybe he thinks that's a real dentist and patient, too. Again, I am very, very concerned.
But as to dad being "on his high horse," I have two more points to make: First, no one under the age of sixty uses the phrase "on his high horse." Maybe because not one in 10,000 Americans will never ride a horse, or knows what distinguishes a "high horse" from any other horse, or sees riding a horse as a status symbol (which is where the phrase comes from.) If you see someone riding a horse today, you either live in the country or in a city that uses mounted police officers. "Because he's driving his Lexus" would be a good update for a modern audience, but I guess the 80 year old writer of this ad doesn't see it that way.
Second, this balding, fat shlub managed to get himself married to someone who produced at least one child for him- a child who talks like an 18th-century villager but a child nonetheless. And despite being super-excited about getting "the best deal" on a phone can afford to own at least two very expensive, luxury pets (if he's "riding his high horse," he must have a lower horse he regularly rides, right? Otherwise it would just be "riding his horse.") Maybe that's why he's on his high horse?