A horse knows when he is going to race.

[GeneD]

A horse knows when he is going to race. How does he know? His breakfast was scanty. (He is angry about that.) He does not have a saddle on his back. He is being led, not ridden, to the grandstand. He is led under the grandstand into an unusual, special stall.
From here: https://owl.english.purdue.edu/exercises/2/1/13/answer

I actually put the correct article in that exercise (the underlined "a"), but I'm not sure it's clear for me why "the" isn't possible here. There is some kind of generalization... The speaker is not talking about all horses in the world, of course, but maybe about all race horses. Would it be possible to change the beginning of the first sentence to "The race horse..."?

Maybe there is some other explanation as to why the "a" is there...

 

[Charlie Bernstein]

The wouldn't be terrible there, but a is better. We use the for universal generalizations: the atom is small, the soldier serves the nation, the magnet attracts iron, the dog is a loyal animal.

So using the there would imply that the writer is talking about all horses, and all horses don't race. So a is the better choice.

It would also be fine to rephrase it this way: The race horse knows . . . .

It's interesting that the writer thinks that all horses are male - and emphasizes it by using he rather than the more correct it.