But I thought we were supposed to avoid the first person, contractions, or certain words! But I thought we were supposed to use the conclusion paragraph to repeat everything from the introduction paragraph!

That was true in high school.  

Your high-school teachers had every reason to lay down artificial rules to teach you habits, helping you avoid real problems: confusing subjective and objective reasoning, or opinion and fact; using unprofessional/immature tone where they were trying to train you to sound like an adult.

Now you are an adult.  (And you should think again about anything you’re articulating with “supposed to”—click here for more.) The bone has grown straight; the artificial cast can come off.  To continue to use those old once-helpful habits at university will create writing that sounds immature at best, and that avoid taking responsibility for words or actions (i.e. removing “I” and using the passive) at worst.  Think of the difference between “I killed your goldfish and I’m sorry” and “Your goldfish has been killed and I am sad that you’re upset.”

You had better, for one, be using the first person in essays you write for me, just as professional scholars in the humanities do — at the very least to formulate sentences like “I will argue, below, that…”. And you had better not waste your conclusion paragraph, in which you should be opening up possibilities for further inquiry, on repetition that suggests your reader (i.e., me) can’t keep an idea in their head for more than five minutes.

Mainly, see rules #5 and #11 here.