she realized that others would see differently:

At first it was downright dulness to Emma. 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. While he was so dull, it was no wonder that Harriet should be dull likewise, and they were both insufferable.

When they all sat down it was better; to her taste a great deal better, for Frank Churchill grew talkative and gay, making her his first object. Every distinguishing attention that could be paid, was paid to her. To amuse her, and be agreeable in her eyes, seemed all that he cared for -- and Emma, glad to be enlivened, not sorry to be flattered, was gay and easy too, and gave him all the friendly encouragement, the admission to be gallant, which she had ever given in the first and most animating period of their acquaintance; but which now, in her own estimation, meant nothing, though in the judgment of most people looking on it must have had such an appearance as no English word but flirtation could very well describe. "Mr. Frank Churchill and Miss Woodhouse flirted together excessively." [...] Not that Emma was gay and thoughtless from any real felicity; it was rather because she felt less happy than she had expected. She laughed because she was disappointed; and though she liked him for his attentions, and thought them all, whether in friendship, admiration, or playfulness, extremely judicious, they were not winning back her heart. She still intended him for her friend.

The last sentence shows that Emma is still thinking that Harriet is the ideal wife for Frank; later we have this conversation between Frank and Emma, when he ask her to find him a wife:

"Very well. I undertake the commission. You shall have a charming wife."

"She must be very lively, and have hazle eyes. I care for nothing else. I shall go abroad for a couple of years -- and when I return, I shall come to you for my wife. Remember."

Emma was in no danger of forgetting. It was a commission to touch every favourite feeling. Would not Harriet be the very creature described? Hazle eyes excepted, two years more might make her all that he wished. He might even have Harriet in his thoughts at the moment; who could say? Referring the education to her seemed to imply it.