A great question, and a complex one. The most simply answer is, it depends on who you're referring to and when in the poem.
To develop that a bit more, the classical Greeks put heavy emphasis on honor. They therefore saw the war as an opportunity to gain honor. They also valued kin relationships and duty; going to war was driven by both. Finally, because the Greeks thought that the gods were directly engaged in human affairs at moments of great importance, they thought the war was in part fated to happen. They would therefore be resigned. However, when the poem opens, the attitude is more complicated. Achilles, for example, clearly thinks that the war is far less important than his personal honor; that's why he withdraws and pouts.
The great Trojan Hector (or Hektor) remains duty bound throughout, and stays committed to the war even when it is clear he will be defeated. That's why his wife Andromache pleads with him not to go. She's lost too many family members, and considers her personal love more important than duty. For Cassandra, the war was inevitable, because she could foresee the future. And it was a tragedy, because she knew the future but none believed her.