Why does Poseidon hold a grudge against Odysseus even though the other gods favor him?
The main reason was that Poseidon favored the Trojans against the Greeks in the Trojan War (the reason for that goes way back to the “beauty contest” between Aphrodite and Helen). When the Greeks won the war, Poseidon took out his frustration and rage (he was always tempestuous) on Ulysses, the “brains” behind the victory. Another complication was how the Greeks were delayed at Aulis until Iphigenia was sacrificed – another dispute among the gods. A good way to understand the whole Trojan was is to examine how the rivalries in heaven among the gods acted out on humans on earth – a primary “belief” in the Greek world.
There is also a very specific, personal reason why Poseidon develops a grudge against Odysseus. On the way back from Troy Odysseus and his men land on the island of the Cyclopes, fearsome one-eyed giants, and he ends up outwitting and blinding the Cyclops called Polyphemus. Polyphemus's father is Poseidon, and he prays to Poseidon to avenge him. Poseidon in that moment conceives a deadly hatred for Odysseus and sets out to thwart him as much as possible. This episode is related in Book 9 of the Odyssey, and also referred to in Book 1.
The problem with the Cyclops answer is that Odyssey's travels began long before that, and the detour to the Cyclops cave was already part of Poseidon's dislike of Odysseus