Odysseus needed to fight in the Trojan war because Paris abducted (or took away) Helen, who was the Queen of Sparta. The problem was that Helen was already married to King Menelaus of Sparta, a whole war was waged against Troy (the city where Paris took Helen) in order to get Helen back.
And since Odysseus was a very cunning and talented warrior and Menelaus' friend, it's rather reasonable that he had to help fight in the Trojan war to rescue Helen.