"The real evils indeed of Emma's situation were the power of having rather too much her own way, and a disposition to think a little too well of herself;"(Chapter 1)

"Highbury, the large and populous village almost amounting to a town, to which Hartfield, in spite of its separate lawn and shrubberies and name, did really belong, afforded her no equals. The Woodhouses were first in consequence there. All looked up to them. She had many acquaintance in the place, for her father was universally civil, but not one among them who could be accepted in lieu of Miss Taylor for even half a day."(Chapter 1)

Others have commented that part of Emma's problem is that she is bored, that her situation offers her so little society. The insular nature of her family & friendships indeed restricted her socializing--but she demonstrates no desire to expand her social options by becoming acquainted with people outside her usual set. I understand that this might have been frowned upon but she appears to me thoroughly invested in the regency caste system.

I think, though, that this cloistered community contributed to Emma's conceit that her intuition & knowlege were sufficient--nay perfect as they were and her well intentioned interference in the lives of others was warranted.

I assume that having a governess meant that she did not attend a school (with those who were both above and beneath her notice), and Mr. Woodhouse's sedentary ways limited exposure to other towns. Therefore her talents, intelligence and accomplishments were never actually compared to those of other similarly trained young ladies. The only opinions of herself and her skills that she hears are those of her father's cherry-picked , amiable friends most of whom would never offer any criticism that might distress DOMW. Mr. Knightley is the only dissenting voice as well as the only person of equal socioeconomic standing.
"Mr. Knightley, in fact, was one of the few people who could see faults in Emma Woodhouse, and the only one who ever told her of them: and though this was not particularly agreeable to Emma herself, she knew it would be so much less so to her father, that she would not have him really suspect such a circumstance as her not being thought perfect by every body."

Why pick Harriet as her intimate friend?

"She was not struck by any thing remarkably clever in Miss Smith's conversation, but she found her altogether very engaging—not inconveniently shy, not unwilling to talk—and yet so far from pushing, shewing so proper and becoming a deference, seeming so pleasantly grateful for being admitted to Hartfield, and so artlessly impressed by the appearance of every thing in so superior a style to what she had been used to, that she must have good sense and deserve encouragement." (Chapter 3)
Harriet is not Emma's intellectual equal any more than her father is. She is pretty. She is deferent. Unlike those in town that Emma knows are not her social equals because they & she know who their parents are, Harriet does not, leaving Emma free to invent equality for her without sacrificing any superiority as she must if Harriet were more accomplished. Mr. Knightly nails it.