Examine the message that Sophocles wanted to convey.
Sophocles wants to communicate the dangers of hubris through Ajax' characterization. A strong warrior, it is pride that ends up ruining Ajax. He believes himself to be the best warrior, worthy of inheriting Achillles' armor. He rejects the assistance of Athena, clearly suggesting that he thinks of himself as better than the divine. He focuses his rage on Odysseus, Menelaus, and Agamemnon, indicating that his pride being offended is reason enough for them to die.
In all of these instances, Ajax's talents and skill- his own sense of arete- is offset by his hubris and belief that he does not need anyone or anything. Sophocles clearly believes that this is his undoing. Ajax seals his doom through his own hand. He cannot be seen as a victim of circumstance because he is so aggressive with his pride. In bringing out Ajax's pride and how it leads to his own destruction, the message becomes clear that excessive pride can ruin individuals. Some level of humility is the key to a happy life, and Ajax's own destruction becomes testament to this idea.