Perhaps Naruto has seen Sakura's shallowness in the past. Maybe she has made comments or decisions that made Naruto feel like she isn't as genuine as he thought. For example, her initial infatuation with Sasuke might seem to Naruto as a rather superficial attraction, which could lead to his coldness.
It could also be that Naruto is trying to protect himself. He might have feelings for Sakura that he doesn't want to admit, and being cold is his way of keeping her at a distance. He may be afraid of getting hurt or rejected if he shows his true emotions, so he acts cold instead.
One reason could be that Naruto is focused on his own goals like becoming Hokage and he might see Sakura's feelings or her actions as distractions. He has a lot on his plate and may not have the time or energy to deal with her in a warm way.
One possible reason could be that Naruto has his own unrequited love for someone else and he is trying to distance himself from Sakura to avoid leading her on. For example, if he has deep feelings for Hinata, he might be cold towards Sakura to make his own feelings clear.
She might be confused at first. Sakura is used to Naruto being friendly and now his coldness would be a big change. She may start to question what she did wrong.
One reason could be that Naruto has been through so much himself and he might think rookies are naive. He's seen the harshness of the ninja world and doesn't want to coddle them. For example, he had to grow up without his parents and faced many life - threatening situations early on.
Sakura might initially be confused. She has known Naruto for a long time and his sudden coldness would be unexpected. She may try to reach out to him to find out what's wrong.
Another reason might be that Naruto has been influenced by external forces. Maybe he has made some bad friends or been involved in some situations that made him think being cold to his family was the right thing. He could have been brainwashed into believing that his family was holding him back from achieving something greater.
One possible reason could be that she might have underestimated Naruto in the past. She often belittled his abilities and dreams, but as she grew and realized his true strength and determination, she felt the need to apologize for her previous behavior.
One possible reason could be extreme jealousy. Sakura might be so blindly in love with Sasuke that she sees Naruto as a threat to Sasuke's attention or her relationship with Sasuke. Maybe she thinks Naruto is getting in the way of Sasuke's return to the village or her attempts to win Sasuke back.
Well, in some fanfics, Naruko's coldness towards Sakura could be a result of a past event. Perhaps Sakura made a mistake that affected Naruko or someone Naruko loves. Another aspect could be the power dynamic. If Naruko is more powerful or has a special ability that Sakura doesn't, and Sakura shows envy or something similar, Naruko might react with coldness.
One possible reason could be that Naruto is so focused on his goal of becoming Hokage. His mind is occupied with training and achieving power, so he seems cold to Sakura. He might not have the time or mental space to show her more warmth.
Perhaps Sakura is in a state of extreme stress. Maybe she has a lot of pressure on her, like trying to save a village or a loved one, and Naruto's actions, which might seem reckless to her at the time, cause her to snap and hurt him without really meaning to.