In my opinion, Agamemnon is quick to "freak out" about Calchas's prophecy because it offends his honor. In the Greek society of this time, a warrior's honor was more important to him than his life. So when Agamemnon feels he is being dishonored, he is quick to react.
The problem in Agamemnon's mind is that his prize is being taken away from him. This prize (Chryseis) is something that he has taken by war (a very honorable thing). If she is taken away from him, it is like his honor is being taken away as well. So Agamemnon reacts in fury -- he does not think that being dishonored in this way will be good for his reputation or his power as leader of the Achaeans.
Actually, in Greek culture of the day, if you had captured somebody in battle, and their family offered to ransom them back it was considered disrespectful to the family of the victim not to accept the ransom, which is why Calachas was so troubled when Agamemnon turned him down. If you read the passage, Calachas was very respectful to the Greek army and did everything just how it should have been done, but Agamemnon broke a sort of unwritten rule but not accepting the money.