Nothing in the Hebrew or the Greek says whale. Hebrew says a great fish, Greek uses a word for a large sea creature, Latin borrows the Greek, and English supplies the species somewhere near the end of that chain.
What Jonah actually says
Now the LORD had prepared a great fish to swallow up Jonah. And Jonah was in the belly of the fish three days and three nights.
Jonah 1:17 (KJV)
The Hebrew is dag gadol. Dag is the ordinary word for fish, the thing a net comes up with, and the King James translates it fish in all eighteen verses of the Old Testament where it appears. Gadol is the plain adjective for large, and Jonah hangs it on other things in the same book: the wind, the tempest that follows it, the city itself.
No species appears in the sentence. A big fish does.
Whale does appear, but never in Jonah
The translators were willing to write whale. They do it four times, and three of those are the Hebrew word tannin, at Genesis 1:21, Job 7:12 and Ezekiel 32:2.
The King James renders tannin dragon far more often than anything else, and serpent a few times. It is the word for what Aaron’s staff becomes in Exodus 7. At Ezekiel 32:2 the translators printed whale in the text and then put their own doubt in the margin: whale, or dragon.
And tannin never occurs in the book of Jonah. In the one story where everybody remembers a whale, the Hebrew never hands the translators the word for a sea monster.
Matthew’s Greek came from the Greek Jonah
The fourth occurrence is the one everybody knows.
For as Jonas was three days and three nights in the whale’s belly; so shall the Son of man be three days and three nights in the heart of the earth.
Matthew 12:40 (KJV)
The Greek word is kētos, and it appears exactly once in the New Testament. I went through the whole of it looking for a second, in two editions, and this verse is the only hit.
Where it does appear is in the Septuagint, the Greek Old Testament, at this very story. When those translators met dag gadol in Jonah, they rendered it kētos megas, a great kētos. So when Matthew reaches for kētos, he is not naming an animal. He is quoting the Greek Jonah, using the word already sitting in the text he is citing.
The Latin makes the chain visible. Jerome writes piscem grandem, a great fish, in Jonah, and then ceti, straight from the Greek, in Matthew.
Something the English hides
Looking for it uncovered a detail no English version shows.
The Hebrew word for the creature changes gender between verses. It is masculine dag when Jonah is swallowed, feminine dagah when he prays from inside it, and masculine again when it vomits him out. Three verses, two forms, and every English Bible I know flattens all three to fish.
Nobody can tell you from the text what that is doing, and I won’t invent a reason. I report it because it is there, and because it is the kind of detail that disappears the moment a translation has to choose one word and stay with it.
Nobody in the story cares what it was
The creature gets four mentions in a book of forty-eight verses, and not one of them describes it. Prepared, swallows, prayed from, vomits. That is the whole of it.
What Jonah spends its length on is a prophet who runs, a city that repents, and a man who sits under a withered plant being angry that God was merciful. When Jesus reaches for the story, the part he presses is not the fish either.
The men of Nineveh shall rise in judgment with this generation, and shall condemn it: because they repented at the preaching of Jonas; and, behold, a greater than Jonas is here.
Matthew 12:41 (KJV)
Because they repented, and a greater than Jonah is here. The sign itself is the three days and three nights, and the verse about the whale’s belly says so outright. This sentence is an indictment, and the one after it repeats the move with the queen of the south: outsiders answered what they were given, and the crowd at home did not.
The argument nobody is having
The whale is an argument people have instead of reading the book. One side proves a whale could hold a man; the other side laughs at the idea. Both are discussing an animal the text declines to name, which is the same argument Genesis provokes by not naming a fruit, and neither side is anywhere near what the next chapter is about.
The other question in the Matthew verse, how the three days were counted, gets asked in the same breath and has a better answer than people expect.
Nineveh believed God and put on sackcloth from the greatest of them to the least. That is Jonah 3:5, and the repentance takes five verses altogether, counting the king coming off his throne and the decree that follows. The book then gives a whole chapter to the prophet sitting outside the walls, furious that the warning had worked and that God had relented.
That is the shape of the thing. Four mentions for the creature, five verses for a whole city turning around, and a closing chapter about a man who would rather have been right. The fish is transport.