Mild spoilers, although I assume most ppl have figured this out by now...
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He's doesn't want to revert to his wolf form because he can't control it. In the past, he has hurt other ppl in that form. He's scared that he'll kill the puppy if he turns back into a wolf. The moment from the previous chapter where he did turn into a wolf was actually a lot scarier for Heesung in the novel. Heesung truly thought the wolf was going to kill and eat him. I feel like the manhwa didn't do a very good job showing how traumatic that moment was for Heesung.
Oooh, yeah, that does make sense. And true, this adaptation really hasn't gotten it quite through, at least in my mind. It felt as if he wouldn't be able to control himself *only* due to the pheromone shock/excess of pheromones/rut timing. In the earlier chapters, I did think the main reason was "not to scare the puppy". But, if he isn't quite in control--ever--in his wolf form, due to the constant high pheromone levels, his upbringing, or whatever else the factors might be; the motives and actions make sense to me. Yeh.
But like for real though, can't he like, just chill in his wolf form? To reduce the instability of his condition?