Why did Cleon say this in the Mytilenian Debate?

In my understanding, Cleon is arguing to kill all the men, even those who didn't instigate the rebellion.

Cleon is arguing to kill all the men because they all willingly took part in the rebellion instigated by the oligarchs.πάντες γὰρ ὑμῖν γε ὁμοίως ἐπέθεντο

In most city-states during the Peloponnesian War, there were two factions: the democratic (pro-Athenian) and the oligarchic (pro-Spartan). Apparently, in the case of Mytilene the democrats joined willingly in the revolt against Athens on the side of the oligarchs. In other cases, the democrats did not take part willingly in revolts against Athens instigated by the oligarchs and either fled, or were overpowered and forced to passive inaction. In such cases, when the revolt was put down, the Athenians typically punished only the instigators (oligarchs) and (re-)installed pro-Athenian democratic governments.

I think this is what Cleon is talking about. He argues that if they only punish the oligarchic Mytileneans and not also the democrats, they would risk communicating to all democratic factions across the Delian League that there is no reason to resist rebellions instigated by the oligarchs. In fact, it would encourage all democrats to join the oligarchs in rebellion in the safety of knowing that, if the rebellion failed, only the oligarchs would face punishment.

Allow me to state a few preliminary points before proceeding to answer.

1. The entire paragraph is available here (MIT Classics Archive). I am using the entire paragraph for better context (reproduced below).
2. Cleon (who was debating Diodotus) was the leader of the pro-faction and wanted to carry out the punishment as agreed (on the day before). Diodotus, the opposing faction's leader, was against it and wanted to re-consider the punishment (presumably because it was too severe).
3. To this day, this event - the Mytilene Debate, is still studied especially for improving oratory, rhetorical and other debating skills. (see 'Why debating still matters', The Guardian, Aug 2016). Therefore, the flow of the argument (and context) is important to understanding their point of view.

Answer:

OP's question:"Or is he (Cleon) really providing a counterargument to his own argument? If so, why?"

No, he was not providing a counterargument. He was merely stating the cost of war and by stating it, he was showing that he - Cleon - was aware of it. He believed Mytilene should still be punished.

Flow of Cleon's Argument:

(the entire paragraph is reproduced below)

1. Mytilene has injured the Athenian alliance by seceding from the alliance.
2. We (the Congress and the Athenian alliance) have been more than fair to the Mytileneans. In fact, we have given them special privileges (in the Athenian alliance).
3. The Mytileneans were not forced into seceding. They did so willingly (voluntarily) and therefore it was "deliberate and wanton aggression".
4. The Athenian's made a mistake by granting Mytileneans special status, we should stop doing this henceforth.
5. Although we might want to distinguish rebels who were forced into rebellion with those who were voluntarily participating in the rebellion because it is too costly (i.e. cost of war) to the alliance to do so -- we still have to fight those of who were forced into rebellion (as opposed to those who did so willingly, like the Mytileneans). In other words, granting special status to allies is too costly and brings us (the alliance) no real benefit. (this is a classic rhetoric style)
6. Therefore, we should still punish Mytilene as agreed.

Book 3, Chapter 9: Fourth and Fifth Years of the War - Revolt of Mitylene

(I have broken the entire paragraph into sections)

...

In order to keep you from this, I proceed to show that no one state has ever injured you as much as Mitylene. I can make allowance for those who revolt because they cannot bear our empire, or who have been forced to do so by the enemy. But for those who possessed an island with fortifications; who could fear our enemies only by sea, and there had their own force of galleys to protect them; who were independent and held in the highest honour by you—to act as these have done, this is not revolt—revolt implies oppression; it is deliberate and wanton aggression; an attempt to ruin us by siding with our bitterest enemies; a worse offence than a war undertaken on their own account in the acquisition of power. The fate of those of their neighbours who had already rebelled and had been subdued was no lesson to them; their own prosperity could not dissuade them from affronting danger; but blindly confident in the future, and full of hopes beyond their power though not beyond their ambition, they declared war and made their decision to prefer might to right, their attack being determined not by provocation but by the moment which seemed propitious.

The truth is that great good fortune coming suddenly and unexpectedly tends to make a people insolent; in most cases it is safer for mankind to have success in reason than out of reason; and it is easier for them, one may say, to stave off adversity than to preserve prosperity.

Our mistake has been to distinguish the Mitylenians as we have done: had they been long ago treated like the rest, they never would have so far forgotten themselves, human nature being as surely made arrogant by consideration as it is awed by firmness.

Let them now therefore be punished as their crime requires, and do not, while you condemn the aristocracy, absolve the people. This is certain, that all attacked you without distinction, although they might have come over to us and been now again in possession of their city. But no, they thought it safer to throw in their lot with the aristocracy and so joined their rebellion! Consider therefore: if you subject to the same punishment the ally who is forced to rebel by the enemy, and him who does so by his own free choice, which of them, think you, is there that will not rebel upon the slightest pretext; when the reward of success is freedom, and the penalty of failure nothing so very terrible?

We meanwhile shall have to risk our money and our lives against one state after another; and if successful, shall receive a ruined town from which we can no longer draw the revenue upon which our strength depends; while if unsuccessful, we shall have an enemy the more upon our hands, and shall spend the time that might be employed in combating our existing foes in warring with our own allies.

Immediately after this, in the very next paragraph, Cleon said: "No hope, therefore, that rhetoric may instil or money purchase, of the mercy due to human infirmity must be held out to the Mitylenians. Their offence was not involuntary, but of malice and deliberate; and mercy is only for unwilling offenders. I therefore, now as before, persist against your reversing your first decision, or giving way to the three failings most fatal to empire- pity, sentiment, and indulgence." -- this my point 6 above.

It should be noted that Cleon wanted to destroy Mytilene; the males killed and the females enslaved. The others are not the people of Mytiline left(because if his policies were to be implemented there would be no one left to rebel) but other Athenian allies. And where he says "ally" you should read "vassal".

which of them, think you, is there that will not rebel upon the slightest pretext; when the reward of success is freedom, and the penalty of failure nothing so very terrible

If you are not harsh against rebellions, most of the people will think that rebellions can only provide rewards with no serious risks. Following orders should not be an excuse; make an example of all of the rebels, and people of other polis will think twice (or thrice) before following their leaders in rebellion.

Basically, the "make our soldiers more afraid of our officers than of the enemy soldiers" inspirational poster.

We meanwhile shall have to risk our money and our lives against one state after another; and if successful, shall receive a ruined town from which we can no longer draw the revenue upon which our strength depends; while if unsuccessful, we shall have an enemy the more upon our hands.

If we are not harsh, our "allies" will keep revolting, we will have to continously fight their rebellions. The only outcomes would be getting a weakened, poorer "ally" or the "ally" becoming free and an enemy. If we are harsh, our "allies" will do as we tell them "because of their own interest".

and shall spend the time that might be employed in combating our existing foes in warring with our own allies

If we do not make an example of those who rebel more rebellions will happen.