I actually considered my question myself, and I concluded that it’s because, when you’re sitting outside the track (as the stands tend to be), the racers pass by you from left to right, which, in our right-handed tendencies, seems more “right.” This is only from inside my own head, I didn’t really discuss this with anyone who would know, but it seems right.
Why are races always run in a counterclockwise direction?
Just so we’re all heading in the same direction.
In jousting contests, the riders pass each other in the direction they’d pass if they were racing counter-clockwise. Both riders have to be on the right if they are right-handed. Any natural lefties would have to conform to the majority.
If this led to races at jousting tournaments traveling in the same direction, people being mostly right-handed could have led to the preponderance of counter-clockwise racing.
I think it comes naturally and is in harmony with the universe. So many other things in nature move counter-clockwise.
For example: - The earth spins counter-clockwise on its axis. The moon orbits counter-clockwise around the earth. The earth and moon together orbit counter-clockwise around the sun, as do all the other planets in the solar system. Our galaxy, of which our solar system is a small part, apparently spins counter-clockwise.
A flock of baby birds contained under a brooder lamp will run counter-clockwise in a circle when they are feeling frightened, chilled or hungry. It’s called kindling when they do that. A flock of birds that kindles in the sky will usually fly in a counter-clockwise spiral.
.
None of those statements are meaningful.
I’m sorry. Can you please elaborate on how they are less meaningful than the other responses?
Perhaps I am not understanding the purpose of this forum and should not be posting here???
The Earth spinning on its axis, the Moon orbiting around it, it orbiting around the Sun, etc, is going to appear to orbit in a clockwise or counter-clockwise direction based on which way you’re viewing it from. If you’re looking at the Earth in such a way that it appears the Moon is orbiting it in a counter-clockwise direction all you have to do is look at the Earth from the opposite side and it appears to be reversed. You can test it with a fist representing the Earth and a finger representing the Moon if you’d like.
Except for Venus and Neptune, I believe I was correct. The Anticlockwise Solar System
It says it right in the page that that is the case only if you view the solar system from above the Earth’s north pole, which is arbitrary. You should do the fist and finger test (you can tell by its name that it’s going to be fun).
Ah so. I stand corrected. Then I guess a race being run in the southern hemisphere would be running clockwise relative to the northern hemisphere. 
Indeed, one definition proposed for “north” on other planets is “the pole that spins counter-clockwise”, though just now it’s not the most popular.
As Cecil points out, European motor racing tracks are usually run clockwise. As a result, most races on the Formula One calendar are clockwise (with some exceptions), although races these days are held all around the globe. Interestingly, when the F1 US Grand Prix was held at Indianapolis from 2000 to 2007, it used a circuit where a serpentine section was combined with part of the oval track, and the oval portion was run clockwise, the opposite direction of the Indy race.
Only guessing, but I would assume it’s because most people are right footed, as well as right-handed. So, they would mount the horse with their right foot. Approaching from the side of the track counter-clockwise would be the best position for the horse.
The thing that really annoys me about clockwise is that it is clockwise. This makes it confusing when you’re trying to learn the unit circle. The angle grows counter-clockwise on the unit circle. To make everything perfect, it would be ideal if 12 was at 3 O’Clock and clocks turned counter clock wise.
I don’t think that is how most people mount a horse - as discussed in another one of Cecil’s columns:
Just to clarify, that’s not actually one of Cecil’s columns, that’s a staff report.
I watched Cheyenne Social Club the other night for the first time. Weirdly, in the final scenes, Henry Fonda’s character mounted a horse on the right-hand side.
I’d say there’s a better than even chance that the shot was flopped, either by accident or intentionally (say, for visual continuity with the prior shot); it happens much more often than you’d think. You always mount from the left unless there’s something seriously wrong with your left leg; a horse can easily spook if you try to mount from the right.
I hadn’t thought of that. I had wondered if he or the director had done it as an inside joke of some kind or to “prove” that left-side horse-mounting is a myth or for whatever other reason just as goofy.
First off, what does “mount the horse with their right foot” mean? Does it mean stiking the right foot in the stirrup, or swinging the right foot over the horse? As has been mentioned, the standard is to stick the left foot in the stirrup and swing the right leg over. Unless you’re sitting sidesaddle, in which you put your left foot in the stirrup, then park your buttocks in the saddle with both legs on the left.
Second, I can’t see how which leg one swings over the horse should have any bearing on which way the horse runs. You might get on the horse well prior to the gate. You can easily turn a horse once you’re on, to face any direction you wish. Or at least if you can’t do that, then you aren’t a very good rider.
Take that up with the people who invented the unit circle. Or take it up with the people who invented the [del]clock[/del] sundail being from the northern hemisphere. “Clockwise” rotates that direction because that is the direction the shadow rotates as the sun goes across the sky. Noon is at the top because that is where the shadow is at noon.
Why the people who devised the unit circle thought the position on the “horizon” on the right and rotating up to the left made sense, I have no idea.
On a side note from the which-wise discussion, the description of the Moon’s path orbiting the Earth is confusing at a minimum. The Moon and the Earth co-orbit the Sun together. Decriptions of relative movement can be ambiguous not only in terms of the direction, but the type of motion as well.