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Our daf cites Rav Ashi who states that a Torah scholar who is not as hard as iron is not considered to be a true Torah scholar. Ravina says that nevertheless, he should conduct himself calmly as the Torah teaches us to avoid anger.
The Gevuros Ari asks from a Gemora in Pesachim which states regarding one who becomes angry; if he is a Torah scholar, his Torah will depart him and yet our Gemora states that a Torah scholar who is not harsh like iron is not considered a talmid chocham.
He answers that if he becomes angry for the honor of Hashem and if it would have been impossible to accomplish this without getting angry; it is not only permitted but warranted. An example for this would be to instill fear into one’s students ensuring that they will not stumble into sin.
We explore the psychology and neurobiology of anger and rage.