Final answer:
Agamemnon offered his daughter Iphigenia for sacrifice to gain favorable winds to sail to Troy, following the seer's declaration that Artemis required it due to Agamemnon's offense.
Step-by-step explanation:
The reason Agamemnon offered his daughter Iphigenia for sacrifice was to gain favorable winds for the expedition to Troy. This was deemed necessary by the seer Calchas, who declared that the goddess Artemis required the sacrifice in order to appease her anger. Agamemnon had offended Artemis by killing one of her sacred deer and boasting about his hunting skills. As a result, the Greek fleet could not set sail for Troy due to the lack of wind, and the sacrificial act was deemed the only solution to propitiate the goddess and allow the Greeks to commence their war against Troy.