The incident in question involved the teacher telling Lizzie that while she did feel bad for her, she couldn't give her a reward for shoddy work to make her feel better about herself. This baffled and angered Lizzie because her favourite means of getting things she wanted stopped working when she got to school. She couldn't trade on her looks, she couldn't whine her way into getting an unearned cookie and a pat on the head and the wrongness of it all settled into her guts and burned. What she took away from school was that teachers were bad people who lived to hurt kid's feelings by expecting them to do the work assigned them.
The end result of being inspired to teach was to give her the impetus to be a wonderful teacher who never wanted to do anything cruel and mean and wrong and hurt the feelings of children by telling them the cruel, horrible, wrong (and CHARACTER-BUILDING) words "I'm sorry but I can't reward failure just to make you feel better about yourself." This, as well as Lynn's need to show us what a good teacher is, is why she fawned over disruptive idiots like Dylan and Jesse and ignored students who actually wanted to learn things. She's a fantasy projection wish-fulfillment of a narcissistic jerk who wanted someone to indulge her whims, not expect her to do the very bad thing of doing things that bored her and ignore people who made her feel bad by
The other end result is to give her another reason to be hostile to that weird Frenchy girl that she has to endure: the unswerving belief that Françoise is trying to make other children feel bad by being smarter than they are because she herself felt that kids who did the work instead of waiting for miracles and trusting in fate and faith did so to be mean to her.