When Pa says of Professor Herbert "He likes me and I like him," why might the two men like each other in "Split Cherry Tree"?
After becoming better acquainted as the day passes that Luster Sexton visits the school, Professor Herbert and Luster reach an amiable understanding of each other and earn each other's respect.
At the end of the school day, a day in which Dave's father has accompanied Professor Herbert around the school, sat in classes, and looked at germs through a microscope, Pa's attitude toward the teacher has completely changed. For instance, he willingly accompanies Herbert into Dave's classes, and he becomes open to what the teacher says and demonstrates. Also, between classes, they speak to each other congenially in the hall.
Luster now realizes that Professor Herbert is an honest, forthright man, who is a good teacher. His hands-on teaching method is effective, Luster understands. And, when Luster reasons with Professor Herbert, whether it be about black snakes or why Dave must pay his debt, Professor Herbert recognizes the truth of what Luster says. In short, the two men respect each other. Thus, "He likes me, and I like him." Further, out of his respect for Professor Herbert, Luster tells his son,
"You are goin' to do as he [Prof. Herbert] says. He's a good man. School has changed from my day and time....I'm behind. I don't belong here."
At the same time, Luster realizes that Herbert has treated him with kindness because he has not reported him as having a firearm, an act which would bring the authorities upon him. Clearly, they have acquired a mutual respect.