I have read Emma several times over the years and have enjoyed the different thoughts put forth by everyone in this and other group reads, and I still must confess I don't see any clear-cut reason for Emma dislike of Jane and visa-versa. It is definitely possible Jane doesn't want to be friends with Emma, even though we don't get much to go on from the ON with regards to that. Jane may be amplifying her natural reserve to be even more "offish" during her interactions with Miss Woodhouse but I guess I don't see any clear reason for her dislike of Emma. I am equally in the dark as to Emma's true motivations and thoughts with regards to Jane. This may be just one of those strange things that happen in life where one simply does not hit it off with someone else and no one, not even the people involved, can clearly define why.