As the saying goes, an elephant never forgets. Is that really true, though? Well, this phrase
sounds more like an exaggeration than it does accurate. While I very much doubt that
elephants can remember things perfectly, the memories of these animals are believed to be
very good. For example, there are reports of elephants being able to remember people or other animals they've been with before, even well after a decade of separation.
Thus this phrase, while an exaggeration, may come from the reputation elephants have of being intelligent animals. The earliest I could find of this idiom in print is from the Wagga Wagga Advertiser newspaper, February 1883:
"And depend upon it such ill-used men like the Delhi elephant, never forget the sting, and seize the first
available opportunity for bespattering the reporters with mud."
Additionally, there apparently is an older expression I've seen mentioned that goes 'a camel never forgets an injury.' While I've never heard of this particular expression before, if the term did indeed exist in the past, then it may be that the phrase 'an elephant never forgets' derived from it, because the wording of both of these expressions are certainly similar.
Note: The above is an animal related saying, and there are plenty more where that came from! For more sayings like this, we have a growing glossary of animal idioms that you might want to check out. It contains an alphabetical list of phrases for each animal. So far, only birds, dogs & cats, and horses have their own category because only these animals, so far, have enough idioms related to them to support a separate category. As more animal phrases are added to the site, that glossary will be updated, so check back another time if you can't find one in particular that you're looking for.
KnowYourPhrase.com - Common Phrases and Idioms with their Meanings and Origins