The author most likely included the information about the principal’s and teachers’ reactions in order to

Below is supposed to be the passage:

It would be rather fun for a change, Millicent mused, getting her books out of her locker in the hall, rather exciting to be part of a closely knit group, the exclusive set at Lansing High. Of course, it wasn't a school organization. In fact, the principal, Mr. Cranton, wanted to do away with initiation week altogether, because he thought it was undemocratic and disturbed the routine of school work. But there wasn't really anything he could do about it. Sure, the girls had to come to school for five days without any lipstick on and without curling their hair, and of course everybody noticed them, but what could the teachers do?

The answer is The author most likely included the information about the principal's and teachers' reactions in order to introduce another character vs. society conflict.

I'll agree with the previous respondent's    The author most likely included the information about the principal's and teachers' reactions in order to introduce another character vs. society conflict.

For the sake of others looking at this question, a bit of history about Sylvia Plath and her short story, "Initiation."  Sylvia Plath (1932-1963) was an American poet, novelist, and short story author.  She struggled with depression throughout her adult life, and ultimately committed suicide.  She wrote The Bell Jar as a semi-autobiographical novel.  She said of that book, "What I've done is to throw together events from my own life, fictionalising to add colour – it's a pot boiler really, but I think it will show how isolated a person feels when suffering a breakdown."

Plath's short story, "Initiation," addresses issues of conforming in order to fit in with friends or societal expectations.  The passage (cited by the other answer posted here) brings the principal and teachers into the picture as an instance of conflict between society and individual expression.