The text quoted in the question is Robert Fagles’ 1990 translation of Iliad 22.126–128. Fagles’ free verse translation is popular, but for poetic effect he often goes a bit beyond Homer’s text. For comparison, here’s the original Greek text and a couple of translations that are closer to the original than that of Fagles:
οὐ μέν πως νῦν ἔστιν ἀπὸ δρυὸς οὐδ᾽ ἀπὸ πέτρης
τῷ ὀαριζέμεναι, ἅ τε παρθένος ἠΐθεός τε
παρθένος ἠΐθεός τ᾽ ὀαρίζετον ἀλλήλοιιν.
Homer. Iliad 22.126–128. Perseus Digital Library.
There is no parleying with him from some rock or oak tree as young men and maidens prattle with one another.
Samuel Butler (1925). The Iliad of Homer, p. 354. London: Jonathan Cape.
In no wise may I now from oak-tree or from rock hold dalliance with him, even as youth and maiden—youth and maiden!†—hold dalliance one with the other.
A. T. Murray (1924). The Iliad of Homer, volume II, p. 463. London: William Heinemann.
† The repetition of παρθένος ἠΐθεός is in the original. Murray comments, “The repetition of the phrase seems best understood as intended to mark the grim contrast between the real and the imagined situation. It is not a mere trick of style.”
So Hector says that he’s not going to talk to Achilles in the manner of a boy and girl ἀπὸ δρυὸς οὐδ᾽ ἀπὸ πέτρης τῷ ὀαριζέμεναι, literally, “to converse from an oak tree or from a rock”. The meaning of this phrase is a puzzle. Fagles interprets it as a boy and girl in love, hiding behind an oak tree or a rock to tell secrets to each other, something that would be childish and inappropriate for warriors about to embark upon hand-to-hand combat. But Allen Benner says that
ἀπὸ δρυὸς οὐδ᾽ ἀπὸ πέτρης ὀαριζέμεναι is a gnomic expression which seems to allude to old folk-stories (e.g. how the first men grew out of trees and rocks). A scholiast† interprets it, “ληρῶδες ἀρχαιολογίας διηγεῖσθαι”, which amounts pretty nearly to ‘make silly gossip over ancient stories.’ Some‡ prefer to interpret the words literally of a maid and a young shepherd talking ‘from an oak or rock’ where they are sitting.
Allen Rogers Benner (1903). Selections from Homer’s Iliad, p. 336, note to line 126. New York: D. Appleton-Century.
† For the scholium, see below. ‡ For example, Fagles, as discussed above.
Rouse, in his translation, gives us an alternative between these two interpretations:
This is no place for fairy tales, or lovers' pretty prattle, the way of a man with a maid, when man and maid prattle so prettily together!
W. H. D. Rouse (1938). The Iliad, p. 258. New York: New American Library.
Let’s have a look at the scholium on line 126, mentioned by Benner above:
ἀπὸ δρνὸς οὐδ᾽ ἀπὸ πέτρης τῷ ὀαριζέμεναι] ληρῶδες ἀρχαιολογίας διηγεῖσθαι, ἀπὸ τοῦ τὸ παλαιὸν ὀρεινόμων ὄντων τῶν ἀνθρώπων ἐκεῖσε τίκτεσθαι, ἢ ἐπεὶ μελιηγενεῖς λέγονται οἱ πρώην ἄνδρες καὶ <λαοὶ> ἀπὸ τῶν λίθων Δευκαλίωνος, ἢ χρησμοὺς διηγεῖσθαι— Δωδώνη γὰρ δρῦς, πέτρα δὲ Πυθων—ἢ περιττολογεῖν, ἀπὸ τῶν περὶ τᾶς δρῦς φύλλων kai περι τᾶς πετρᾶς κυμάτων.
from oak or from rock to converse] to relate silly ancient legends, as from the ancient mountains that brought forth men, or the ash-born men now called <men [λαοὶ]> from the stones [λίθων] of Deucalion, or, as they say of the oracles, from the tree of Dodona, or the rock of Python, or beyond that, from the leaves around the oak or the waves around the rock.
Ernest Maass, ed. (1888). Scholia Graeca in Homeri Iliadem Townleyana, p. 283. Oxford: Clarendon Press.
The legends that the scholiast thought that Homer might be alluding to are the myth of autochthony (that people originally sprang from the earth like plants); the myth of Deucalion and Pyrrha (the survivors of a great flood, who threw rocks over their shoulders which became men and women); the oracle of Dodona (where according to Herodotus a dove “settled on an oak tree, and there uttered human speech”), and the Omphalos of Delphi (a rock sacred to Apollo, under which the Python was said to have been buried by the god).
In my opinion, the fact that the scholiast did not seem to know which myth Homer was referring to, rather undermines this interpretation.