Achilles reacts to the deception. In this first reaction, he seems to have ideological reasons for his anger.
Subtitles in this scene read:
I was taught to uphold right over wrong... ...in words as well as deeds. I shall obey the Atreids if their command is just. If not, I shall oppose them. Call me the basest man in Greece... ...son not of Peleus, but of hell... ...if I lend myself as cover to their plots.