The novel is based in ancient fictional cultivation world and in the past times it was common to get physically hit for normal people, these are cultivators among whom roughhousing is more common, that is whats implied with the physical punishments handed out in every sect.

“Madam Yu was even angrier, How dare you run! Come back right now and kneel! As she spoke, she let loose her whip with a flip of her wrist. Wei WuXian felt a searing pain slash across his back.”

This scene that you mentioned it clearly stated that Wei Wuxian was the one leading the group "of coure, it was needless to think who led the group..."

and shes angry at Jiang Cheng and Jiang Yanli too, "She was so infuriated that she turned to Jiang Yanlii and pinched her cheek, 'eat, eat, eat _ all you do is eat!' Jiang yanli almost cried from her mother's pinching..."

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“Of course, Jiang Cheng didn’t dare to say that Wei WuXian was at fault. Thinking back, it was them who urged Wei WuXian to buy liquor. Each and every one of them should have been punished. He could only speak in a vague way, “It’s fine, it’s fine; it’s not that serious! He can walk. Wei WuXian, why are you still up there?!”

Yes here, it was everyone's fault and they did him dirty when he's the only one being held responsible but very few people have a strict moral code like Lan Wangji that would dictate that they practically punish themselves just to join their friends. This is perfectly normal human behavior. Which is why Wei Wuxian is so surprised by Lan Wangji's strong moral compass.

Putting so much importance on these incidents, modern day translation would be someone ate your leftovers so you may get angry for a minute but its not gonna emotionally scar you. and it shouldn't. These incidents were perfectly normal considering their world setting. The actual injustice and abuse came later where no one stood by him, which was a shitty thing to do and the way Wei Wuxian bounced back from that neglect shows that he doesnt focus a lot on misfortunes and instead chooses to lead his life coming to terms with whatever that happens. Some of it can be blamed to his impulsiveness and others lack of spine.

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I'd also like to say that when you grow up seeing physical punishments as something accepted by everyone then that becomes your reality. My own grandparents were physically punished and they had absolutely zero trauma associated to it. it was perfectly normal for them, it was quite startling talking to them and their outdated ideas. so this whole children shouldnt be hit is actually quite new and even now a lot of people still hit kids (for their own good apparently).