And the idea that they quarreled because Jane was jealous of Emma, is also Emma's idea.

But if Jane had always understood that Frank adored her, if the idea that Jane was jealous is totally in Emma's imagination, that Frank has taken the blame for their quarrel and given Emma as the cause, rather than blame his beautiful wife's powerful temper, or his reluctance to trust his own father with a secret that would break his Aunt's heart - then the very scene where Frank appears to be at his worst, flirting most shamefully with Emma, is actually the one where he is most earnestly begging, and declaring his love to Jane Fairfax.

The writing of chapter 43 deliberately obscures the stated fact, that when Emma and Frank are accompanied only by Harriet, Frank has nothing to say to Emma, and in fact "She had never seen Frank Churchill so silent and stupid. He said nothing worth hearing -- looked without seeing -- admired without intelligence -- listened without knowing what she said."(43)

What is written as a merry tete-a-tete between Frank and Emma, is actually a forlorn attempt to engage the whole group in conversation. Mr Weston, Miss Bates and Emma are happy enough to promote Frank's scheme, but he unintentionally insults Mrs Elton by giving Emma precedence, and Mr Knightley hates him and sees only an evil influence not to be encouraged, and Emma insults Miss Bates, and Jane Fairfax has already said what she had to say yesterday and has not the pliant temper to be worked on by tricks, and until she can speak openly, is resolved to be silent.
And what is he saying to Jane?
"Don't say I was cross. I was fatigued. [Your] heat overcame me... I am perfectly comfortable to-day."
[Emma usefully answering on Jane's behalf]"You are comfortable because you are under command."
"Your command? Yes." I can have no self-command without a motive. You order me, whether you speak or not. And you can be always with me. You are always with me."(43)

Unfortunately he goes on after these passionate, tender, softening words to add: "I say nothing of which I am ashamed,I saw you first in February. Let every body on the Hill hear me if they can. Let my accents swell to Mickleham on one side, and Dorking on the other. I saw you first in February."(43)

Such a reminder of his discretion and the safety of their secret, at such a time, could only irritate Jane and remind her of what she is obliged to endure for the sake of secrecy. And when she finally, reluctantly, is forced to respond (if only to stop this nonsense) and sternly warns him "it can be only weak, irresolute characters, (whose happiness must be always at the mercy of chance,) who will suffer an unfortunate acquaintance to be an inconvenience, an oppression for ever."
His assurance of his constant dependence on her judgment would not have mollified her, as comes with an (amusing but) ill-timed joke at the expense of Miss Woodhouse's judgment "Well, I have so little confidence in my own judgment, that whenever I marry, I hope somebody will choose my wife for me. Will you? (turning to Emma.) Will you choose a wife for me? I am sure I should like any body fixed on by you."

His reminding her of his hopes the day before to tell his father as soon as he had arranged to ship his aunt to the doctors on continent, where she could not be distressed by any unseasonable revelations, is just talk, his attempt to work on her fears for him in the face of the tyranny of distance over the next couple of years, just infuriating to a woman who has been stuck in Highbury listening to such rubbish all year, to no effect. His claims of being totally enslaved by her excellent judgment, are infuriating when they are camouflaged by this false show of wit and impudence. It would take a woman with a perfect temper, and no judgment at all, to bear him.

Of course, Frank makes it very clear in his letter to his father that "it was a quarrel blameless on her side, abominable on mine"(50), that he was the angry one, and she the injured ... but what was he to say? The truth? That his aunt was very like Mr Woodhouse, and with her poor health, low spirits and dependence on her darling child; that reconciling her to the knowledge would be a formidable and time-consuming task; that Frank must find a way of gradually talking her around to the idea of his getting married, making her happy with it, over the next couple of years. That until he could find some way of ensuring his father's discretion, he must therefore keep the engagement a secret even from his father, because Mr Weston has a gob on him, and even his affection for his son could not surmount his desire to go around London cheering (Homer Simpson voice) "In your FACE, Mrs Churchill" at so fair an opportunity.

And how could he decently explain his lady's heart?
That Jane's objection had been Frank's failure to tell his father of their private understanding, keeping her hanging around Highbury month after month on the promise of it, obliged to suffer the kind attention and hospitality of the Westons (when she can't escape to the Eltons), and observe how all their dearest plans will be upset by her, while he comes up with one excuse after the other why he couldn't trust his father this time, how he has arranged a better way to tell him next time?
That they argued because she was tired of waiting around for him to overcome what she considered feckless, spineless qualms about his fathers discretion, while she was every day giving the Westons more and more reason to suspect her of dishonesty and cold ambition? And that she had finally decided that if he thought she was going to keep hanging around Highbury waiting for him to get around to it all summer, if he thought she was as addicted to talk and adverse to action as himself, he had better have another think coming?