Why do you think Nick is trying to prove that “ain’t” is a word in Frindle?
I think that it is because his teacher, Mrs. Granger, appears to be trying to stop her students from calling pens "frindles." It is revealed later in the book that she was only opposing it to make the word more popular, but at the time, Nick sees her opposition as a huge barrier.
Mrs. Chatham, the principal of Lincoln Elementary, explains to Nick that Mrs. Granger doesn't want him and other students to use the word "frindle" because it isn't a word, like "ain't." This causes Nick to look "ain't" up in the dictionary and prove that it is a word. By proving that "ain't" actually is a word, he feels that he has more evidence for his argument that he should be able to call pens "frindles" if he wants to.
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