It is fairly obvious in Chapter XLIII of Great Expectations that Pip and Drummle are rivals for the affection of Estella. Much like two male animals, they eye one another briefly, then, when Pip espies Drummle blocking the fire's warmth from him, he squares off against his rival by planting himself shoulder to shoulder before the fire, and neither man gives way to the other until Drummle finally departs.
After looking down at Pip's boots and chuckling in, perhaps, a subtle innuendo about Estella's remark about Pip's coarse boots as a boy (as she may have told him), Drummle derogates the remote countryside from which Pip comes implying that it is so very uncivilized:
"...I mean to explore those marshes for amusement. Out-of-the-way-villages there, they tell me. Curious little public houses--and smithies--and that!"
After Drummle tells the waiter that he will not dine that evening because he is "going to dine at the lady's," Pip, employing the imagery of a fierce dog, states,
Then, Drummle glanced at me with an insolent triumph on his great jowled face that cut me to the heart, dull as he was, and so exasperated me, that I felt to take him in my arms (as the robber in the story-book is said to have taken the old lady) and seat him on the fire.
When Drummle "rubs it in" that he, not Pip,is going to be with Estella, Pip can hardly control himself; so, he tells Drummle he never did wish to enter into any conversation with him, Drummle warns him not to lose his temper as he has "lost enough without that." With arrogance he bites off the end of his cigar, goes out to mount his horse, leans down to have a man light his cigar while glancing sneeringly through the window at Pip, who later leaves "out of sorts." Indeed, there is a deep antipathy between Pip and the dark Drummle.
Pip encounters Bentley Drummle at the Blue Boar Inn, and after failed attempts on each man's part to pretend he doesn't see the other, the two quickly enter into an awkward and uncomfortable conversation. Essentially, Drummle indirectly belittles Pip for having grown up in the marsh country, and flaunts his relationship with Estella in Pip's face, saying, "The lady won't ride to-day; the weather won't do...And I don't dine, because I am going to dine at the lady's."
Ultimately, Pip, who has disliked Drummle since the two met, suggests "that we hold no kind of communication in the future." The thought of Estella being with Drummle is too much for Pip to bear, so he decides that the two should not talk anymore. Drummle agrees, saying, "Quite my opinion, and what I should have suggested myself, or done-more likely-without suggesting."
So, while the two can't agree on much, they agree that they have no need to communicate with each other.