I am not saying that Emma was undilutedly correct in her opinion of Miss Jane Fairfax. No one who reads the book can think so. (Similarly, Mr. Knightley, when he eventually discovers Harriet's good qualities, was still not wrong about her being not clever, and being easily lead. He just needed to see past that to learn about her principles, and domestic proclivities.)

But: had Mr. Knightley forced Emma to spend time with a reserved, cold person who had accepted no overtures of Emma's, nor offered any of her own, how could Emma have derived any pleasure from the acquaintance? And how could Mr. Knightley expect more than 'just attentions' from Emma to Jane Fairfax? He seems to have wanted them to be bosom friends; he implies that all the obstacles to such a friendship were put up by Emma; he sees nothing but diffidence and proper behavior in the reserve that Emma finds no way to break through during a social evening of exactly the type of attentions he wishes Emma to offer; he thinks he would be proved right about the acquaintance, despite obvious and repeated proofs that neither one desires it, and that both of them would be thanking him for his interference if they merely tried doing things his way. Rather arrogant.

Emma should have been more attentive, both to Miss Fairfax and the Bateses, but she should have been allowed to choose warmth and returned interest in her friends without Mr. Knightley's disapprobation. To paraphrase Mr, Knightley himself:

I agree with [Mrs. Weston] entirely that it will be a much better thing [to let Emma chuse her own intimates]. Invite [Jane Fairfax] to dinner, Emma, and help [her] to the best of the fish and the chicken, but leave [her] to chuse [her own level of intimacy]. Depend upon it, a woman of [one-and-twenty] can [decide for herself].