Achilles Weakness

In books 16-18, I feel like Achilles weakness is shown when Petrakolas goes to battle pretending to be Achilles. If Achilles was really a strong leader he would just stop whining an fight for his people, but instead he lets Petrokolas die. If Achilles had just sucked it up and fought then he probably would not have died and neither would Petrokolas. Even though Achilles asked Zeus to protect Petrokolas and help him win it was still selfish of Achilles to let him go in the first place. I just think it makes Achilles look like a zero and makes Petrokolas look like a hero. Achilles is a demi god and he needs to start acting like it instead of crying to his mommy.