Help with Questions to The Iliad: in Book 9, Achilleus first threatens to

In Book 9, Achilleus first threatens to sail home the next day, but then changes his mind. At the same time, he has revealed another change of mind: although he initially refused to fight until the Trojans set fire to the Achaian ships, now he says he won’t fight until they set fire to the ships of the Myrmidons. As it turns out, he lets Patroklos lead the Myrmidons into battle when only one ship of the Achaians has been torched. How do you account for his first two changes of mind, and why does he let Patroklos fight?