The reason why Jews don't eat octopuses is because octopuses are not Kosher and when a food is not Kosher it does not fit under the Jewish dietary laws.
Under the Jewish dietary laws also known as (Kashrut), any water creature is only considered to be kosher if the water creature features and possesses both scales and fins.
And so because octopuses lack both scales and fins they are not considered kosher and so the octopuses are strictly forbidden to consume by the Jews and Jewish law.
The Jewish law and rules, according to Leviticus 11:9, anything that lives in water must have scales and fins to be eaten by Jews.
The rule for Jewish law for Kosher foods, excludes all shellfish and cephalopods, like squid, shrimp and lobster, as well as fish that are scaleless, like eels, catfish and sharks.
Strict Jewish dietary laws (Kashrut) prohibit the consumption of specific animals, animal byproducts, and any mixtures of meat and dairy.
The 3 widely recognized foods that Jews cannot eat include:
Pork: The consumption of pork, bacon, and ham is strictly forbidden.
According to the My Jewish Learning Kosher Guide, land animals are only permitted if they have split hooves and chew their cud.
Pigs possess split hooves but do not chew their cud.
Shellfish & Non-Kosher Fish: Shrimp, lobster, oysters, and crab are all prohibited.
To be considered kosher, seafood must have both fins and scales.
Meat and Dairy Mixtures: Combining meat and dairy at the same meal is forbidden.
This includes serving a cheeseburger or having a dairy cream sauce over chicken.
Kosher law dictates that observant Jews must wait several hours after eating meat before they can consume any dairy products.