Diaphanus says:

“I can give you some information about the Classical Greek and Latin(ized) forms of the word.

It is true that oktopodes (masculine and feminine) and oktopoda (neuter) are the normal (nominative) plurals of the Greek word oktopous, but the funny thing about the word pous (“foot”) is that while its true stem is pod- (third declension), it had a shorter stem po- (second declension). This would also apply to its compound words.

The Romans themselves latinized Greek words and treated them as Latin words by giving them Latin endings, so the argument about how octopi is incorrect because it is a latinized Greek word treated as a Latin word was dreamt up by someone unfamiliar with Latin grammar. So, the “mistaken notion” here is the idea that octopi is problematic because it has a Latin ending.

The word polypus (“many foot”), from pous, was latinized and had the shorter stem polypo-. You would think that its plural would be polypodes, but it has the plural polypi.

Octopodes is the plural according to the true stem of the word octopus, but octopi is the latinized plural according to the shortened stem.

Octopi isn’t really any more incorrect grammatically than polypi. It’s just going by an unusual, but nevertheless existing, shorter form of the word.

On a related note, the Superorder name Octopodiformes uses the true stem (octopod-), but the Family name Octopoteuthidae uses the shorter one (octopo-).”