One reason could be for power. Combining their strengths through marriage could make them an even more formidable force. Maybe Sasuke saw it as a strategic move to protect their village or to face some greater threat that they are not aware of yet.
In some cases, Sasuke could be angry. He might see Naruto's request as a sign of weakness or as Naruto giving up too easily. He could lash out at Naruto, telling him to fight instead of asking for death. However, he would still be deeply troubled by the request and would probably struggle with it for a long time, constantly thinking about whether or not he should consider it.
He might be initially confused. Sasuke is not used to Sakura ignoring him as she has always been somewhat persistent in her attention towards him. So, he may be at a loss as to why she is suddenly acting this way.
Well, in some fanfictions, Naruto might use his shadow clones to search every possible location. Once he locates Sasuke, he could use his strong bond and persuasion skills to convince Sasuke to come with him. Naruto might remind Sasuke of their past friendship and the dreams they once shared, like protecting the village together.
One reason could be that Sasuke realizes he needs Naruto's unique abilities. Naruto has the Nine - Tails' power which could be useful in a certain task. So he takes Naruto with him to achieve a common goal.
Well, they might go on an adventure to discover new jutsus. Sasuke could be on a mission to learn more about his clan's secrets and takes Naruto along for the ride because he knows Naruto's strength. Maybe they'll encounter powerful enemies and have to rely on each other to survive.
He could also be initially confused. Sasuke has known Sakura for a long time, and this unexpected act from her would leave him wondering about her motives. He may hold back his anger for a while to hear her out and understand why she did such a thing.
It could be that there are rumors or false information that lead Sasuke to have this thought. Or perhaps Naruto's actions are misinterpreted by Sasuke.
The relationship would evolve from a deep friendship and comradeship to a romantic partnership. They would have to be more open with each other about their feelings. Sasuke might become more protective of Naruto in a different way, not just as a friend in battle but as a future life partner. Naruto would also be more likely to confide in Sasuke about his insecurities and hopes for the future. Their bond would be strengthened further as they face the challenges of being in a relationship in the ninja world, like dealing with the opinions of other ninjas and the political implications of their union.
Naruto might initially be in denial. He's so used to having Sakura around and believing that they have a future together. So when she leaves for Sasuke, he might think it's just a temporary thing or that she's been influenced by something or someone. But as time passes and he realizes it's real, he would be deeply hurt. He might also start to question his own self - worth, thinking that he wasn't good enough for Sakura. And he might even try to win her back at first, but then slowly come to accept the situation and focus on his other responsibilities like being a ninja and protecting the village.