This is echoed in what follows in 4.2 where Celsus writes - "But that certain Christians and (all) Jews should maintain, the former that there has already descended, the latter that there will descend, upon the earth a certain God, or Son of a God, who will make the inhabitants of the earth righteous, is a most shameless assertion, and one the refutation of which does not need many words."
Observe, now, that if he had wished with a kind of apparent force to subvert faith in the prophetic writings, either with regard to the future or past advent of Christ, he ought to have set forth the prophecies themselves which we Christians and Jews quote in our discussions with each other (τῷ διαλέγεσθαι πρὸς ἀλλήλους).
Does Origen limit himself to 'face to face' meetings or 'discussions' here or does he have in mind broader 'attacks' made against one another? I think the latter. I think 'discussions' or 'dialogues' is far too specific here. Indeed the mirroring of this terminology with the word 'attack' in Celsus makes this absolutely clear in 4.30:
Observe how this venerable philosopher, like a low buffoon, turns into ridicule and mockery, and a subject of laughter, the announcement of a divine judgment, and of the punishment of the wicked, and of the reward of the righteous; and subjoins to all this the remark, that such statements would be more endurable if made by worms and frogs than by Christians and Jews who quarrel with one another (διαφερομένων ἀπαγγελλόμενα)! We shall not, however, imitate his example, nor say similar things regarding those philosophers who profess to know the nature of all things, and who discuss with each other (καὶ πρὸς ἀλλήλους διαλεγομένων περὶ τοῦ), the manner in which all things were created, and how the heaven and earth originated, and all things in them; and how the souls (of men), being either unbegotten, and not created by God, are yet governed by Him, and pass from one body to another; or being formed at the same time with the body, exist for ever or pass away.
Origen clearly means to mimic what is said first about Jews and Christians in a counter attack against the philosophers. Here Origen does not mean 'dialogue' or 'discuss' but something more akin to 'address openly' and rhetorically like a philosopher or groups of philosophers.
To this end we reach what I consider to be the original place where the Jew made his introduction in Celsus's treatise - at the point Celsus writes:
Celsus appears to me to have heard that there are treatises in existence which contain allegorical explanations of the law of Moses. These however, he could not have read; for if he had he would not have said: The allegorical explanations, however, which have been devised are much more shameful and absurd than the fables themselves, inasmuch as they endeavour to unite with marvellous and altogether insensate folly things which cannot at all be made to harmonize. He seems to refer in these words to the works of Philo, or to those of still older writers, such as Aristobulus. But I conjecture that Celsus has not read their books, since it appears to me that in many passages they have so successfully hit the meaning (of the sacred writers), that even Grecian philosophers would have been captivated by their explanations ... After this, selecting from all the treatises which contain allegorical explanations and interpretations, expressed in a language and style not to be despised, the least important, such as might contribute, indeed, to strengthen the faith of the multitude of simple believers, but were not adapted to impress those of more intelligent mind, he continues: Of such a nature do I know the work to be, entitled Controversy between one Papiscus and Jason, which is fitted to excite pity and hatred instead of laughter. It is not my purpose, however, to confute the statements contained in such works; for their fallacy is manifest to all, especially if any one will have the patience to read the books themselves. Rather do I wish to show that Nature teaches this, that God made nothing that is mortal, but that His works, whatever they are, are immortal, and theirs mortal. And the soul is the work of God, while the nature of the body is different. And in this respect there is no difference between the body of a bat, or of a worm, or of a frog, and that of a man; for the matter is the same, and their corruptible part is alike. Nevertheless I could wish that every one who heard Celsus declaiming and asserting that the treatise entitled Controversy between Jason and Papiscus regarding Christ was fitted to excite not laughter, but hatred, could take the work into his hands, and patiently listen to its contents; that, finding in it nothing to excite hatred, he might condemn Celsus out of the book itself. For if it be impartially perused, it will be found that there is nothing to excite even laughter in a work in which a Christian is described as conversing with a Jew on the subject of the Jewish Scriptures (Χριστιανὸς Ἰουδαίῳ διαλεγόμενος ἀπὸ τῶν ἰουδαϊκῶν γραφῶν), and proving that the predictions regarding Christ fitly apply to Jesus; although the other disputant maintains the discussion in no ignoble style, and in a manner not unbecoming the character of a Jew.
This would tend to support the reading of διαλεγόμενος to mean 'debating' or 'discussing.' But I think Origen means here that the debate is carried on the lofty manner of philosophers - i.e. the way they debate one another viz. 'with high rhetoric' - which certainly precludes the application to what the Jew says about Jesus.
Look at the next few examples - little children and ants:
But as, in what follows, Celsus, not understanding that the language of Scripture regarding God is adapted to an anthropopathic (ἀνθρωποπαθοῦς) point of view, ridicules those passages which speak of words of anger addressed to the ungodly, and of threatenings directed against sinners, we have to say that, as we ourselves, when talking with very young children (νηπίοις διαλεγόμενοι), do not aim at exerting our own power of eloquence, but, adapting ourselves to the weakness of our charge, both say and do those things which may appear to us useful for the correction and improvement of the children as children, so the word of God appears to have dealt with the history, making the capacity of the hearers, and the benefit which they were to receive, the standard of the appropriateness of its announcements (regarding Him).
and again:
For, speaking of the ants conversing with one another (διαλεγομένων ἀλλήλοις), he uses the following language: And when they meet one another they enter into conversation (ἀλλήλοις διαλέγονται), for which reason they never mistake their way; consequently they possess a full endowment of reason, and some common ideas on certain general subjects, and a voice by which they express themselves regarding accidental things. Now conversation (διαλέγεσθαί) between one man and another is carried on by means of a voice, which gives expression to the meaning intended, and which also gives utterances concerning what are called accidental things; but to say that this was the case with ants would be a most ridiculous assertion.
The range of meaning clearly goes beyond 'dialogue' for as Origen notes ants don't have discussions. Something is represented here which
Now, by such statements, this illustrious philosopher Celsus distinctly slanders the Christians, asserting that, when the Jews press them hard, they acknowledge the same God as they do; but that when Jesus legislates differently from Moses, they seek another god instead of Him. Now, whether we are conversing with the Jews (Ἰουδαίοις διαλεγόμενοι), or are alone with ourselves, we know of only one and the same God, whom the Jews also worshipped of old time, and still profess to worship as God, and we are guilty of no impiety towards Him.
and again in the discussion of a Dialogue of Plato:
For Plato introduces Socrates conversing with Crito (Σωκράτης Κρίτωνι διαλεγόμενος) as follows: 'Must we never do injustice to any?' 'Certainly not.'
and again:
He further supposes, that because we join along with the worship of God the worship of His Son, it follows that, in our view, not only God, but also the servants of God, are to be worshipped. If he had meant this to apply to those who are truly the servants of God, after His only-begotten Son,— to Gabriel and Michael, and the other angels and archangels, and if he had said of these that they ought to be worshipped,— if also he had clearly defined the meaning of the word worship, and the duties of the worshippers,— we might perhaps have brought forward such thoughts as have occurred to us on so important a subject (ὡς περὶ τηλικούτων διαλεγόμενοι).
and again:
Besides, is it not most absurd and inconsistent in you, on the one hand, to make so much of the body as you do— to expect that the same body will rise again, as though it were the best and most precious part of us; and yet, on the other, to expose it to such tortures as though it were worthless? But men who hold such notions, and are so attached to the body, are not worthy of being reasoned with (οὐκ ἄξιον τοῦτο διαλέγεσθαι); for in this and in other respects they show themselves to be gross, impure, and bent upon revolting without any reason from the common belief. But I shall direct my discourse to those who hope for the enjoyment of eternal life with God by means of the soul or mind, whether they choose to call it a spiritual substance, an intelligent spirit, holy and blessed, or a living soul, or the heavenly and indestructible offspring of a divine and incorporeal nature, or by whatever name they designate the spiritual nature of man. And they are rightly persuaded that those who live well shall be blessed, and the unrighteous shall all suffer everlasting punishments. And from this doctrine neither they nor any other should ever swerve.
and again:
Moreover, Celsus thinks that he ought not to reason (μὴ διαλέγεσθαι) with those who hope for the good of the body, as they are unreasonably intent upon an object which can never satisfy their expectations. He also calls them gross and impure men, bent upon creating needless dissensions. But surely he ought, as one of superior humanity, to assist even the rude and depraved. For society does not exclude from its pale the coarse and uncultivated, as it does the irrational animals, but our Creator made us on the same common level with all mankind. It is not an undignified thing, therefore, to reason (Ἄξιον οὖν διαλέγεσθαι) even with the coarse and unrefined, and to try to bring them as far as possible to a higher state of refinement— to bring the impure to the highest practicable degree of purity— to bring the unreasoning multitude to reason, and the diseased in mind to spiritual health.
I think from all these examples the correct sense that Origen has is 'engage' which goes back to the primary meaning of διαλέγω in Liddell:
A.pick out, Hdt.8.107, 113, X.Oec.8.9, etc.; πτῶμα glean fallen olives, PFay.102.20; cf. διαλέγειν: ἀνακαθαίρειν, Hsch.; select, separate, Pl.Lg.735b; examine, check documents, PFay.11.26 (ii B.C.), etc.
From this detailed examination of all the uses of διαλέγω in Against Celsus I think it is by no means certain - and in fact unlikely - that Origen was saying that the Jew was portrayed as standing in front of Jesus 'debating' or 'discussing' his birth from a virgin. Instead I think Origen means that the Jew was attacking Jesus in a childish manner, openly and out loud like a Cynic in the marketplace.
“Finally, from so little sleeping and so much reading, his brain dried up and he went completely out of his mind.”
― Miguel de Cervantes Saavedra, Don Quixote