That wikipedia page seems to blame the toxicity of some avacado parts to their content of persin. According to the page on persin:
Persin is a fungicidal toxin present in the avocado. It is generally
harmless to humans, but when consumed by domestic animals in large
quantities it is dangerous.
Even in the case of animals, wikipedia suggests that it is the Guatemalan variety which is responsible for the reports of poisoning, not the Mexican variety. This is corroborated by an article which explains that the concern over the toxicity of avacado leaves originated with a 1984 study at the University of California at Davis. This study found that the consumption of very large amounts of avacado leaves was toxic to goats. However, an author of the atudy (Dr. Arthur Craigmill) clarified that the leaves in question were those of the Guatemalan avacado (Persea american), and that the toxic effects were not observed when goats were fed Mexican avacado leaves (Persea dryminfolia).