In some fanfics, it could be due to a conflict over a magical object or a spell. Suppose Lily finds a powerful magical item and wants to use it in a way that Harry thinks is dangerous. This difference in opinion might lead to Harry yelling at her to stop her from doing something reckless.
It could also be related to a relationship issue. If there are romantic feelings involved between them or someone else in the story, jealousy or hurt feelings might cause Harry to yell. For instance, if Lily starts spending a lot of time with another character and Harry feels left out, he could lash out at her in anger.
One reason could be Ruby's lack of respect for Weiss's family name or heritage. Maybe Ruby made a joke that Weiss found offensive about her family's reputation in the world of Remnant. So, Weiss yelled at her to show her dissatisfaction.
Perhaps in this fanfic, Harry has been influenced by dark magic or some evil entity. This external influence could distort his perception of Lily and turn his normal feelings for her into hatred. Dark magic has the power to corrupt one's mind and change relationships in unexpected ways.
Maybe Harry finds out that Dumbledore knew more about his family's past than he let on. For instance, if Dumbledore had information about some dark secrets in the Potter family but didn't tell Harry, it could make Harry furious and prompt him to yell. Also, if Dumbledore's actions led to the death or harm of someone Harry cared about, like Sirius, Harry would likely be very angry with him.
One possible reason could be that Mrs. Black has said or done something to endanger his friends. For example, if she reveals some secrets that put Ron and Hermione in danger, Harry might yell at her out of anger and protectiveness.
In some fanfics, it could be due to a threat she believes she can't protect Harry from. Maybe she thinks that by leaving him, the dark forces won't target him as much.
One possible reason could be a plot device to create drama. Maybe the author wants to show a rift between them for the sake of a more complex storyline. For example, if there's some misunderstanding or a secret that has come to light which makes Harry act this way.
In the fanfic, Lily's fairy heritage could make her a target for dark forces. Harry, being the hero he is, would then vow to protect her. Their relationship would grow as they face numerous challenges together, and Harry might learn some new spells or techniques from Lily's fairy magic along the way. This would not only strengthen their bond but also make Harry a more powerful wizard.
Perhaps they misunderstand Sakura's relationship with Naruto. They might think she has romantic feelings for him when Naruto's parents have other plans for their son, so they yell at her to keep her away.
Perhaps they are blackmailed. A powerful dark wizard could threaten to harm all of their friends and family if they don't abandon Harry. They may feel they have no choice but to sacrifice their relationship with their son to protect others they care about.
One possible reason could be an alternate universe scenario. Maybe in that fanfic's universe, there are dark forces at play that make Lily and James act out of character and ignore Harry. It could also be a plot device to create a more angsty or dramatic story, where Harry has to face challenges without the support of his parents.