This is the first time anyone seems able to give answers. Snape must remain measured so he adheres, word by word, to the guidelines set by both masters. If he engages with Harry, if he forgets himself, he could accidentally reveal something that gets them in trouble. Harry must not interrupt. Snape must remain in control of the interaction and for once, it’s not because he wants to wield power over Harry. The danger is what makes Snape angry here, not his dislike of Harry.
