Montag regrets losing his temper as it signifies his understanding that forceful confrontation is ineffective and has only contributed to his feelings of despair, isolation, and shame.
Montag regrets losing his temper with the women because this outburst represents a pivotal moment where he recognizes the futility and harm in aggressively confronting those who are not open to change. At this point in the narrative, Montag is overwhelmed by the contradictions within his society and his role as a fireman. His anger at the women’s blindness to the oppressive state of their world leads to a confrontation which ultimately serves no purpose but to deepen his despair and feeling of isolation.
Through these interactions, Montag realizes that forceful opposition is not the way to enact change, and he feels a profound sense of sorrow and pity for the women who are immersed in ignorance. The regret he experiences is accompanied by a shame for having lost control and an understanding that change cannot be achieved through intimidation or anger but perhaps through more subtle, thoughtful means.
This internal conflict directly correlates with Montag’s wider struggle throughout the book, as he seeks understanding and a path to make a meaningful difference in an indifferent or hostile environment.