The commenter has suggested that Jonah was a false prophet because he said, "Forty days more and Nineveh shall be destroyed" (3:4), and this didn't actually happen. This makes him a false prophet (according to the commenter) because Deuteronomy 18:21-22 says:
If you say to yourselves, "How can we recognize an oracle which the Lord has spoken?", know that, even though a prophet speaks in the name of the Lord, if his oracle is not fulfilled or verified, it is an oracle which the Lord did not speak. The prophet has spoken presumptuously, and you shall have no fear of him.
Well, that sounds like an open-and-shut case, but I propose that it's not.
First we must consider what Jonah was commanded to do.
This is the word of the Lord that came to Jonah, son of Amittai: "Set out for the great city of Nineveh, and preach against it; their wickedness has come up before me" (1:1-2).
What did Jonah do? He fled. He ran in the other direction. "But Jonah made ready to flee to Tarshish away from the Lord" (1:3).
Why did he do this? We don't have to guess; he tells us. After Nineveh had repented and God relented from judging them, Jonah "became angry":
"I beseech you, Lord," he prayed, "is this not what I said while I was still in my own country? This is why I fled at first to Tarshish. I knew that you are a gracious and merciful God, slow to anger, rich in clemency, loathe to punish." (4:1-2).
Jonah was angry because God spared them, and he knew from the very beginning that if the people of Nineveh repented, that God would do that very thing. And basically God confirms in 4:11 that this is how he works, and certainly how he was working with respect to Nineveh:
Should I not be concerned over Nineveh, the great city, in which there are more than a hundred and twenty thousand persons who cannot distinguish their right hand from their left, not to mention the many cattle?
It's a rhetorical question, obviously: of course God is concerned for them. That's why he sent Jonah!
On the other hand, though, Jonah clearly hated the Ninevites: he knew that God would be merciful to them if they repented (4:2), he didn't want that to happen, and so he fled in the other direction so as to avoid (if possible) any chance of being involved in the deliverance of Nineveh. When God made it clear that he couldn't run away, then Jonah repented.
The only question that remains for the "false prophet" proposal comes up now. After Jonah was vomited out of the fish/whale onto the beach, God tells him again: "Set out for the great city of Nineveh, and announce to it the message that I will tell you" (3:2, emphasis added). We know (3:3) that Jonah obeyed God as far as going to Nineveh was concerned. The only question left for the present discussion is: Was Jonah's message in 3:4 the one that God commanded in 3:2 or not?
"Forty days more and Nineveh shall be destroyed."
3:10 tells us that God relented from destroying the city because they repented. Therefore Jonah's "prophecy" didn't come true. So he's a false prophet, right?
Wrong (with all due respect to the commenter).
Either God told him to preach this message or he didn't. Clearly God told him to preach something (3:2), so either this was it, or it wasn't.
If it wasn't, then Jonah didn't preach the message that God commanded. He preached something else, and so it would seem that he could be called a false prophet. But it is simply inconceivable that Jonah didn't preach the message that God commanded. In the first place, he had originally refused to preach at all, and so he tried to flee to Tarshish. But he repented of this, and instead he went to Nineveh in obedience to God. But for Jonah to have preached some other message than one that God commanded would mean that he didn't really repent at all: his "repentance" would be a foul-weather one no better than Pharaoh's various "repentances" over the plagues in the book of Exodus: "I repent [with crossed fingers, until these present bad times are over]." But there is nothing in the book of Jonah to suggest this. In fact, the evidence suggests nothing of the sort: God didn't criticize him for what he preached, and Jonah basically says (4:2), "I knew this would happen. I knew if I went and did what you told me to do, they would repent, and you would relent from judging them. And that's what happened!" And really, the only criticism of Jonah in chapter 4 has to do with his attitude, not what he preached: in other words, God reproves him for his sin (his anger), but not for what was not sinful (his message).
In short, then, it's clear from the "wrap-up" in chapter four that Jonah preached exactly what God wanted him to preach. And it seems completely incredible to suppose that Jonah's repentance wasn't complete; there is no evidence for that at all in the book.
The only alternative that remains is that the message Jonah preached in 3:4 was exactly what God wanted him to preach. Well, how can that be, if Deut. 18 says that a true prophet's prophecies have to come true?
I think it's clear that we have to say that it is not a prophecy per se, but rather a warning: "God will destroy this city [unless you repent.]" This makes perfect sense with what Jonah says in 4:2-3. It makes perfect sense with God's response to Jonah in 4:11. It makes perfect sense with the fact that God had to have given him this message: clearly it couldn't have been intended as a literal prophecy, so it must have been something else, and it makes perfect sense as a warning.
We have another very similar example with another prophet. Please see how the horribly wicked king Ahab - the most evil king Israel ever had - repented when Elijah prophesied his doom.
"Have you seen how Ahab has humbled himself before me? Because he has humbled himself before me, I will not bring the evil in his days; but in his son's days I will bring the evil upon his house" (1Kings 21:29, but start reading with verse 17).
Other similar examples: God tells Abraham that he'll spare Sodom if he finds fifty - no, forty-five - no, forty - no, thirty - no, twenty - no, ten righteous men there (Genesis 18:16-33). Which is it? Well, it's not that God doesn't know what he's going to do. He answers prayers, and he answered Abraham's. But the Ninevites prayed, too (Jonah 3:8). This doesn't make Jonah a false prophet any more than God's answer to Abraham's prayer in Genesis 18 made God a liar in what he first told Abraham.
Or how about Numbers 14, where God says:
How long will this people [i.e., Israel] despise me? And how long will they not believe in me, in spite of all the signs which I have wrought among them? I will strike them with the pestilence and disinherit them, and I will make of you [i.e., Moses] a nation greater and mightier than they (Num. 14:11-12).
God said he was going to destroy them and reject them, and make a greater nation from Moses' descendants. But that's not what happened. Moses prayed for them, and God relented. Does that make God a liar? Of course not! And in the same way, the fact that the Ninevites repented doesn't make Jonah a liar or a false prophet. His message was God's message to them: his word to them, just as Moses and Abraham received similar messages of judgment which (in response to prayer) God later "modified" (not that God literally changes his mind, which is ridiculous - but that's a subject for some other post!)
When it comes to "prophecies" that come upon people threatening judgment, there is frequently (I can't say always, but I might say "almost always") a condition attached - often unspoken: unless they repent. So there is just no reason to suggest that Jonah was a "false prophet" because his warning didn't come to pass: it didn't come to pass because the people repented, and because God is slow to anger, and abounding in mercy. This is a great and wonderful thing for us as well: when we sin horribly, and do monstrous evils, we absolutely must not suppose that God will not receive us if we repent. We are never so wicked that God will not forgive us if we repent.