[The Illiad] Why doesn't Menaleus carry a dagger with him?

I'm reading the Illiad, and I just got to the part where Paris and Menelaus fight in single combat so that the armies of Troy and Greece don't need to fight. Menelaus seems to have Paris defeated, but when he strikes Paris's helmet with his silver-studded sword, the sword shatters. Then Menelaus drags him by his helmet, but the strap breaks and Paris gets rescued by the gods.

My question is... Why doesn't Menelaus have a dagger or knife? Shouldn't everybody in the ancient world carry a knife of some kind of them, pretty much everywhere they go?