It could be someone from the village who doesn't understand Naruto's need for solitude. Maybe a council member who thinks Naruto is shirking his duties and tries to force him back into the spotlight.
Perhaps it's a new enemy who is attracted to Naruto because of his power. This antagonist might not care that Naruto wants to be left alone and keeps provoking him, forcing Naruto to either fight or keep running to find a truly peaceful place.
There's a possibility that the main antagonist is an internal force within Naruto himself. His desire to be alone could be a manifestation of some dark part of his psyche. This 'inner antagonist' could be trying to make Naruto cut himself off from his loved ones completely, leading him down a path of self - destruction. And Naruto has to fight this internal battle while also dealing with any external threats that come his way during his isolation.
The main antagonist could be an internal one - Harry's own guilt. It's like a dark shadow that follows him everywhere. He wants to be alone to escape from it, but it keeps haunting him. It makes him question his every move and decision, and it's this internal struggle that could be seen as the main 'antagonist' in the fanfiction as it constantly opposes his desire for peace and solitude.
In this fanfiction, Naruto may find himself in a situation where he's being hounded by people for various reasons - some for help, some for his power. He simply wants to be left alone to live a normal life. So he might start to avoid the village and the people in it, seeking refuge in a secluded place. There, he could explore his own thoughts and feelings more deeply, perhaps even learning new skills or abilities on his own, away from the watchful eyes of his friends and the village.
Maybe Naruto has had enough of the chaos in the ninja world. He could be tired of all the battles and political intrigue. So, he decides to find a secluded place, perhaps a small island, where he can live in peace and train by himself without any distractions.
It could be a new and powerful dark ninja who thrives on isolation and wants to keep Naruto alone. He might see Naruto's solitude as a weakness to be exploited.
It could be someone who took advantage of Kushina's leaving. Maybe a rogue ninja who wants to use Naruto's vulnerability to their advantage. They could try to turn Naruto against the village by making him believe that the village drove Kushina away.
Maybe the main antagonist is actually a group of people within Konoha. They might be some of the elders who think Naruto's isolation is a threat to the village's stability. So they send people after him to bring him back, which Naruto sees as an intrusion and they become the antagonists in his eyes.
Maybe an ancient evil ninja who was sealed away long ago but has now been released. This antagonist could have powers that nullify any communication or summoning jutsu, forcing Naruto to fight alone. He would be extremely powerful and know many forgotten and deadly jutsu.
It could be other powerful ninja clans who see the fem Kyuubi's possessive behavior towards Naruto as a threat to their own power and influence. They might try to separate them.
It could be a powerful ninja from another village who sees Naruto's godlike powers as a threat to his own plans of domination. Since Naruto is already feeling vulnerable due to his family leaving him, this antagonist might try to take advantage of his emotional state.