The concluding sentence is: “it takes a much cleverer man to be a really good animal doctor than it does to be a good people's doctor.”
Yes, I agree — for one strong reason: an animal doctor gets no case history. A human patient walks in and says, “I have had a headache for three days and light hurts my eyes.” A horse can only stand there. The vet must reach the same conclusion from swelling, gait, breathing, appetite and the look of the eye alone. That takes sharper observation, not less.
The story backs the horse up: the vet over the hill had six weeks and still missed a plain problem of eyesight, while Dolittle solved it in one conversation.
The other side, fairly stated: One could argue that a people's doctor faces harder cases in some ways — patients hide symptoms, exaggerate, or refuse treatment. So the honest answer is that the two jobs are differently difficult. But on the horse's own point — diagnosing without words — it is clearly right.