On page 7 when Itsuki says, "Today's full moon is really pretty, don't you think?" and then he had kind of a stunned expression, then tells her she needs to study more, is something that doesn't translate too well without context.
In Japanese, the phrase, "月が綺麗ですね" or "suki ga kirei desu ne" literally means "The moon is beautiful, isn't it?", but it's used as a figure of speech and can also mean "I love you."
In the late 1800s/early 1900s, Japanese people were even more reserved than they are at present day and hesitated to express feelings of love directly. It is said that Japanese novelist and teacher Natsume Soseki (Who lived in those times) said when he heard his student translated the English "I love you" into "ware kimi o aisu" (ware means I, kimi means you, and aisu means love): "Japanese people don't use such an expression, you should say 'the moon is beautiful isn't it?'."
So basically, Itsuki unknowingly confessed her love to Futarou, which is why he replies that she needs to study more - because if she knew more about Japanese literature and English, she would have not said what she did.