Of all her matchmaking deeds, I think Emma's rejection of Robert Martin it truly the worst. She is prejudiced against him from the start. In chapter 4:

"He is very plain, undoubtedly -- remarkably plain: -- but that is nothing, compared with his entire want of gentility. I had no right to expect much, and I did not expect much; but I had no idea that he could be so very clownish, so totally without air. I had imagined him, I confess, a degree or two nearer gentility."

RM does not fit "her" idea of the perfect man, therefore he cannot be right for Harriet. This is one of the most childish and arrogant assumptions Emma makes. Her lack of experience really shows here.

And once she has passed judgment on him, she won't go back on it, despite proof that he is indeed a very good sort of man and would do perfectly for Harriet. She let's her vanity get in the way: another example of her inexperience and of what happens when her actions are no longer contained by the counsel of good friends. Emma, emboldened by the departure of Miss Taylor, fancies herself now a "grown-up" and acts with the arrogance of one who is certain to be "right". She has yet to learn that Miss T's departure is not a validation that she, Emma, is now a grown-up. Emma fails to recognize she still has much to learn.