In the Torah, anger is the Hebrew word harah. But in many verses, the word is paired with ahff – connecting to the nostrils.
What do nostrils have to do with anger? The Torah tells us: G-d formed a Human from the soil’s humus, blowing into his nostrils the breath of life: the Human became a living being. (G. 2:7)
So anger that is paired with ahff is connected to the nostrils; harah ahff is anger from the soul.
So it makes sense that every single example of G-d’s wrath uses the word ahff – because G-d is spirit, after all! The most important interactions G-d has with us are spiritual in nature, showing G-d’s intentions and wishes. That in turn connects with the part of us, the divinely-gifted soul, that we have through our nostrils.
And we can see in the text that when man is similarly righteously angry, the Torah also uses the word ahff. Jacob uses it with Rachel when she demands children (G. 30:2). Potiphar is described this way when his wife tells him of Joseph and the intended adultery (though whether Potiphar is mad at Joseph or his wife remains ambiguous) (G. 39:19). Judah even uses it when he is trying to forestall Joseph from being angry at the brothers (G. 44:18). And Moshe is harah ahff when Pharoah is deceitful – and again when he sees the people worshipping the Golden Calf (E. 11:8, 32:19). Balak and Bilaam are both described this way as well (N. 22:27, 24:10). In all cases, the person’s anger shares commonality with G-d’s righteous wrath.
But there are ten verses where man’s wrath is not described as being ahff, and they tell a different tale.
We have “please do not be angry” examples where the speaker clearly does not believe anger would be justified: Avraham negotiates with G-d on Sodom : “Let not my Lord be angry,” (G. 18:30,32). Rachel takes much the same approach when she tells her father, Lavan, to, “not be angry that I cannot get up” (G. 31:35). Joseph similarly warns his brothers, after he reveals his identity, to “not be angry” (G. 45:5) (perhaps he recalls that the last time the brothers were angry in this way (see below), they put an entire town to the sword) In all of these cases, anger, because it is not paired with ahff is not like G-d’s righteous anger.
There is another category of anger that is not ahff: anger that comes from pride. This anger is indignation from being mistreated, but it is not, the Torah seems to be telling us, sourced from the soul. We have Cain, who is consumed with an unjustified jealous rage (G. 4:5,6). Jacob is angry at Lavan’s trickery (G. 31:36). And the brothers are angry that their sister was taken by Shechem (G. 34:7). In the Song at the Sea, the people also sing of G-d’s pride: In Your great triumph You break Your opponents; You send forth Your fury (harah), it consumes them like straw (E. 15:7). Moshe is also angry – but again from pride in his ethics, not soulful righteous anger: Moses was much harah and he said to GOD, “Pay no regard to their oblation. I have not taken the donkey of any one of them, nor have I wronged any one of them.” (N. 16:15).
All of these describe prideful anger. Note that pride is not necessarily wrong; it is just not the same as truly anger from the soul.
P.S. There are 30 verses with harah ahff, and 10 verses with just harah. G-d is angry 14 times in the text, and we are warned of G-d’s consequential anger 8 additional times.