How to evaluate someone's knowledge? From Yongey Mingyur Rinpoche teaching I came to understand that non-judgmental observation of situations and aversion of attachments is the way to get rid of sufferings. Then how would a teacher evaluate a student's knowledge on anything?
In traditional schools and colleges there are grading systems. Students are assigned grades according to their exam results. How are students evaluated in Buddhist monasteries?
I believe (based soley on what you've written) that Mingyur Rinpoche is talking about our first reaction to new stimuli: in the first moment of perception there's an unlanguaged, felt sense (vedana) that whatever we are perceiving favors or threatens us which gives rise to attachment or aversion. Simultaneously, there's an awareness of what we perceive (samjna) followed by a host of associations that go with it (prapanca) which leads to further kleshas and conceptualizations (anusaya) which incline (cetana) us (anusaya) toward action (karma). This process is what keeps us trapped in samsara.
On the other hand, determining whether someone understands the lesson they've been given on the five skandhas, or the Utarratantra Shastra - while entailing the same processes - inclines the mind toward liberation. That is, what drives the process is the wish that whomever is receiving the teaching may understand it and benefit from it.
Having been a monk, and having been in both the role of student and teacher in a monastic college (and Mingyur Rinpoche visited my monastery twice while I was there), I can tell you that the point of a Buddhist education is to sharpen one's prajna in order to recognize the constituents of experience and to recognize reality for what it is. Seeing things as they are - as opposed to how we think they are makes us much less reactionary, and much more content.
So, in the end, there is absolutely no contradiction between assessing whether or not a student grocks the meaning of a text, and striving to meet whatever one encounters with equanimity.