Answer:
The main reason that Dr. Natterson-Horowitz gives to explain this, it's from a psychological perspective.
Basically, the psychology of a human patient is way too different from animal patients. Human patients are treated under controlled environments, while animal patients are treated in their natural habitat most of the time, like oceans and jungles.
Similarly, to treat animal there's needed another skills to have succes, because they act according to their instincts, that's what probably Dr. Natterson-Horowitz tries to explain when she gives a psychological perspective of such difference between both treatments.