Between Mr Knightley and Emma, and also in Regency society, on whether a woman really had the right to choose her husband entirely on her own and for herself, or whether she should be guided by her friends and family.

The Prince Regent, for example, (whose own marriage was arranged by his father), had had his Government announce the engagement of his only daughter and heiress, Charlotte Augusta (aged 16), to Prince William of Orange (22 year old,the son of King William I of the Netherlands) in December 1813. Charlotte initially made no public contradiction of her fathers wishes, but was rumoured to have formed a secret alliance with Prince Frederick of Prussia (19 year old General of the Cavalry and nephew to the King of Prussia). Certainly he was in England as part of the King's entourage for the meeting of the Allied Sovereigns in June 1814, when Charlotte publicly called off her engagement to the Prince of Orange.
Her father made himself beastly to her and to his subjects (especially his female subjects) by shutting her up until she agreed with him, re-opening the 'delicate investigation' into his wife's private life, merely to provide himself justification for forbidding her seeing and comforting her darling child in this season of trial, refusing his wife accommodation if she remained in England, but granting her an increased allowance if she left the country. Queen Caroline left for the continent that July, not seeing her daughter then, or ever after.
The Princess was not without supporters- Byron visited her and wrote verses for her,creating a huge stir in February 1814, when he added 'Lines to a Lady Weeping' to his first edition of the Corsair, implying that the battle between father and daughter was a political one along party lines. There were calls that he be hung for treasonous sentiments, and Princess Charlotte won enthusiastic support of the opposition in Parliament as a consequence - it is possibly due to their pressure on the matter in parliament that she (prisoner of politics that she was) was allowed to visit the sea for her health in September 1814, albeit at Weymouth, when she had wanted Brighton.
The stand-off ended suddenly in December 1815, when Prince Frederik announced his engagement to Princess Louise of Anhalt-Bernburg (there had been rumours in the papers in August 1813 that he was preparing to marry "a Princess of Austria, sister to the Empress Maria Louisa", which makes me wonder if the romance with Princess Charlotte was really just one in a series of newspaper speculations on who the Prince would marry).
While Princess Charlotte continued to oppose a marriage to the Prince of Orange, the father and daughter could agree that Prince Leopold of Saxe-Coburg and Gotha might do instead. He was a Russian cavalry officer who had been diligently applying his diplomatic skills to wooing the Princess, the Prince, the Royal family, the ministers, and any relevant diplomats since he had met her (Like Prince Frederick, he was at the the meeting of the Allied Sovereigns in June 1814, but as part of the entourage of the Emperor of Russia).
While the Prince Regent did not like the Thungrian prince's penury and lack of royal connections, he thought well of him and took little more than a year to relent and approve the match. The happy couple wed in May 1816, by which time they had become the most popular Royals of the day by (in the public imagination) marrying only for love.
It might be some consolation to the ghost of Prinny to know that Prince Leopold made good his deficiencies by becoming Leopold I, King of Belgium when the opportunity arose, and by successfully organizing a match between his sister and the Duke of Kent, and later between her daughter and his nephew (the second son of the duke of duke of Saxe-Coburg and Gotha), by which means gathering quite a number of Royal connextions, but these developments could not have been foreseen by him or by Jane Austen.

But back to Emma and Mr Knightley- Mr Knightley expresses a batchelor's opinions of women and marriage on a number of occasions. Mrs Weston has, in his opinion, received a good education from Emma on "the very material matrimonial point of submitting your own will, and doing as you were bid."(5). And his presumption in "He is desperately in love and means to marry her.(7) is seized on by Emma ("but is he sure that Harriet means to marry him?"(7))- although Emma is consistent only in her opposition to Mr Knightley, and as likely to run with the hound as the hare on Harriet's right to choose.
I like to think his beliefs brought him some grief; or at least that the complacency of Mr Elton's looks were as much motivation as his brother's weather forecast, for walking (very quickly) "some way along the Highbury road"(15) before returning to assist Emma in settling their relatives - if he had taken his cue from Emma's expression a short consultation with the coachmen might have been sufficient.
The sexism also shows in his opinion on Frank Churchill's conduct: "If he would act in this sort of manner, on principle, consistently, regularly, their little minds would bend to his"(18) This comment nominally includes the uncle but the subject is how best to manage the temper of the aunt.
When it is just Emma and himself, he can't resist a little sexist abuse -- "I have still the advantage of you ... by not being a pretty young woman"(12) or "Nonsensical girl"(26) -- none of which has any perceivable effect on Emma's behavior or her sense of self - apart from provoking her to argue with him, or to consider on reflection how mistaken he is.
Neither of them appear to be 'winning' at this point, although the authors critique of Mr Knightley is not as obvious as that of Emma - Emma's interference in Harriet's affairs is exposed as causing grief, Mr Knightley's interference in Emma's affairs is merely causing no good.