Also, it's hard to overstate the importance of honour in the society of the Iliad. One way of looking at it is this: these warriors have essentially exchanged their chance at an ordinary life, their future, everything for the chance of achieving honour and glory through battle. Their honour is kind of all they have left, which is why they get so touchy it is threatened. If they don't have their honour, what is the point of fighting? What do they have to gain from risking their lives?

In modern society, we don't really have the same concept of war being heroic and honourable. Particularly after the horrors ofWorld War I, we've become disillusioned and cynical about these ideals. This can make it hard for modern reasons to relate to the characters, but once you get into the warrior mindset that honour is important above all, the poem and it's characters become easier to relate to, in my opinion.

(Which is not to say that Homer just mindlessly promotes the ideals of the warrior society...Like you've pointed out, Hector facing Achilles wasn't the most practical choice. And Achilles also acts irrationally when his honour is threatened, and ends up paying a terrible price when Patroclus is killed. I think rather, The Iliad is neither a straightforward glorification nor critique of the society it portrays (and of war generally), but rather shows it in all it's complexities and tragedy. It's the kind of grey morality that I tend to be find lacking in most fiction)