The two were never close, but responsibility fell on Shikamaru’s head to man the mission to bring Sasuke home. Why does Shikamaru rescue Sasuke?
Shikamaru has to rescue Sasuke because Hokage Tsunade personally requested him. All Jonin are away on other missions, so she places the Sasuke-retrieval mission on the newly Chunin Shikamaru.
Tsunade instructs him to gather as many Genin as he needs and to leave the village immediately.
She also encourages Shikamaru to bring Naruto on the mission to rescue Sasuke. It may be likely that other squad leaders wouldn’t want Naruto along, but Shikamaru isn’t high enough rank to decline Naruto. The two have a rapport already and Tsunade knows Naruto would be upset if the leader of Sasuke’s retrieval mission would not want him.
Shikamaru is instructed to rescue Sasuke
In chapter #182, the fifth Hokage, Tsunade, invites Shikamaru to her office. She informs him that Sasuke Uchiha is fleeing from the Village and is likely heading to the Village Hidden in The Sound. Sasuke finally decides to give himself to Orochimaru for the sake of power and the advancing of his curse mark’s potential.
Tsuande says the assignment needs immediate action and there will likely be trouble. There is a good chance that Orochimaru’s henchmen are helping Sasuke travel between lands and reach their facility.
Shikamaru thinks to himself that the idea of retrieving Sasuke has already become tiresome. “Among my peers, he was outstanding in every respect,” Shikamaru thought. “He was certainly superior to me.”
He suggests to Tsunade the format of a four-mean team, composed of Jonin and at least Chunin. She rejects this idea, reminding Shikamaru that all other Jonin are away on other missions.
“Within the next half an hour, gather as many Genin as you deem necessary, and leave the village.”
Lady Tsunade to Shikamaru | Chapter #182
Shikamaru thinks that although the mission is a drag, he can’t just ignore it. He believes it’ll surely work out one way or another.
So that’s the answer. Shikamaru has to rescue Sasuke because Hokage Tsunade personally asked him. All Jonin are away on other missions, and Shikamaru is put in charge as the available Chunin.