benutzen (more commonly: verwenden) is used for objects you can touch, while nutzen rather applies for ideal, abstract or non-physical things. You use duolingo to learn German – Du nutzt duolingo, um Deutsch zu lernen. To use an unique opportunity – Eine einmalige Chance nutzen. Wir nutzen den Lehrer seems incomplete, since it doesn't obey this rule and how would you use a person? Person A taking advantage of/exploiting person B (with a negative connotation) would be benutzen or ausnutzen. Wir nutzen das Wissen des Lehrers, um unsere eigenen Kenntnisse zu erweitern – We use the teacher's knowledge to extend our own proficiencies, this would be legit.