Alligator pear is another name for the avocado.
The American Heritage Dictionary entry for Alligator Pear is:
"By folk etymology from American Spanish aguacate, avocado (the trees are said to grow in areas infested by alligators)."
In the Nahuatl language of the Aztecs, the word for the fruit of the avocado tree was 'ahuacatl.' Spanish speakers pronounced it 'aguacate', but other Spanish speakers substituted the form 'avocado' for the Nahuatl word because 'ahuacatl' sounded like the early Spanish word 'avocado' (now 'abogado'), meaning "lawyer." In borrowing the Spanish 'avocado', first recorded in English in 1697 as "avogato pear."
Neither the skin nor the alligators are the sole source of the likely origin of alligator pear. In the opinion of the Oxford English Dictionary, the most likely origin is simply the mispronunciation of the Nahuatl word for the fruit "ahuacatl," and sites the following (among others): 1861 Tylor Anahuac ix. 227 "There is a well-known West Indian fruit which we call an avocado or alligator-pear, and which the French call 'avocat' and the Spaniards 'aguacate.' All these names are corruptions of the Aztec name of the fruit, 'ahuacatl.'"
I believe all three - the skin, the alligators and mispronunciation all contributed to the development of the name 'alligator pear.'