One reason could be exhaustion. Naruto has been through a lot in the original story. In a fanfic, if he is continuously put through more and more difficult situations without proper breaks, he might just give up out of sheer tiredness.
One reason could be the sacrifices he has to make for the village. Naruto is so dedicated to protecting Konoha that he might feel he doesn't have time for love. His responsibilities as Hokage are immense, and he has to constantly be on guard against threats. Another reason could be past traumas. He has lost many people he cared about, like Jiraiya. This could make him afraid of getting close to someone again and losing them, so he gives up on love.
One possible reason could be that Naruto realizes Sakura's true feelings for Sasuke are unwavering. After many attempts to win her heart, he might come to the conclusion that he's just chasing after someone who will never love him back. So, he decides to give up and focus on other aspects of his life, like his ninja duties or his friendships with other people in the village.
Maybe Naruto gets tired of always chasing after Sasuke. He has his own life and dreams too. He might think that he has sacrificed enough of his time and energy on Sasuke, and it's time to focus on himself and the village. He could start to believe that Sasuke has made his own choices and he can't keep forcing Sasuke to come back.
If Naruto gives up on his friends in a fanfic, it would be a huge departure from his character. Naruto is known for his unwavering loyalty. His friends are his strength. Without them, he might become a much darker and more isolated character. He could lose his drive to become Hokage as his friends were a big part of that motivation. Also, the village that values friendship and bonds might see him in a different light, and he could face a lot of ostracism.
The dynamic between Naruto and Sasuke would be completely different. Instead of the usual pursuit, there would be a sense of finality. Naruto might start to avoid Sasuke, which would change the way Sasuke views Naruto too.
The story could take a dark turn. Without his heart, Naruto might become a soulless being, and his friends would be devastated. They might try to find a way to get his heart back. Maybe they search for a powerful sage or some ancient magic that could reverse what has been done.
It could also be due to a misunderstanding. Some false information might have spread in the fanfic's world, making Naruto believe that everyone has turned their backs on him. Like, some bad guys framed his friends, and Naruto, being unable to see through the lies at first, gives up on everyone in despair.
Well, it makes him more cynical. Normally, Naruto is a very positive and hopeful character. But in this fanfic, giving up on everyone would turn him into someone who doubts the goodness of people. He would become more withdrawn and less likely to reach out to others.