In the book Anne of Green Gables, what is the climax or major crisis between Anne Shirley and Gilbert Blythe. There are at least 2 incidents...

The scene between Anne and Gilbert in which he calls her "Carrots" and she smashes a slate over his head is the beginning of their conflict.  In a typical plot structure this incident, along with Gilbert's having to rescue Anne, represents the rising action.  The climax or turning point occurs when there is a change in the conflict between the two characters.  Anne really wants to score the highest on the entrance examinations to Queens.  She wants her name to be above her longtime rival.  However, she ties with him, and that seems to be enough, because at this point her thinking about Gilbert starts to change.  She won't admit it to others, but she thinks how pleasant it would be to have a friend like Gilbert who is her intellectual equal. At this point in the novel, she has finally put aside her pride and accepted Gilbert for the intelligent and decent person that he is.