What is an instance in the Odyssey when Odysseus acts against the advice of his men?
There are several instances in the epic of Odysseus going against the advice of those around him, but perhaps the most disastrous was the time in Book IX when Odysseus decided, against the wishes of the men with him, to stay and "claim a gift" from the Cyclops
Odysseus had landed at the island of the Cyclops. He was excited by the reputation of the Polyphemus, the son of Poseidon, as a cruel and inhuman creature. Odysseus, ready to show his bravado, decides that just stealing cheese from Polyphemus' cave is cowardly; he wants to stay and confront the Cyclops.
This decision leads to disaster -- Polyphemus traps Odyssseus and his men in his cave, and proceeds to eat four of his men. While they are trapped Odysseus prepares a plan for getting out f the cave. Doing so involves permanently blinding Polyphemus and tricking him. Odysseus's decision to stay and face the Cyclops was disastrous for everyone, and Odysseus and his remaining men only narrowly escaped.