The antropomorphism of animals dates to ancien Egypt. Then, they were deified. In the 19th Century, we see masters such as Grandville, Beatrix Potter, Kley, notably Daumier and Dore (who illustrated the Fables of La Fontaine) humanizing animals in their respective styles, and are said to have influenced Walt Disney, who brought a lot from Europe. Humanized animals however, only become endearing with Disney cuteness. For me, this trait resulted from the identification of toy, babyhood and animal nature.
I guess it is because in Walt Disney, playfulness, childhood and nature were at one.