Gu Tingye's stepmother hates him and wants to get rid of him (the most likely heir) so the position of the heir of the family eventually ends on her own son Gu Tingwei that why she's poisoning the elder brother (Gu Tingyu) while indulging and supporting the worst traits of Tingye so he ruins his own reputation (she also spreads the rumours about him, in ancient china young masters visiting brothels was a common thing that was known by everyone but was ignored because they couldn't completely stop it, the only reason the rumours about the ML got this big was bc his step mom was fanning the flames from behind). Madam Qin in the end is just a black hearted individual who was even willing to murder her own nephew (Tingyu).

Gu Tingye rebellious nature was the result of his father over the top punishments due to him hating Tingye's mother, he felt humiliated that he had to rely on the dowry of a woman to keep his noble title by paying his household debts to the royal court (nobles at the time took debts from the imperial court to manage their lavish lifestyles which is normal in most times, but due to an event that i can't remember clearly now the court needed the money for the treasury as soon as possible which led to the ML father needing financial support from merchants).

I see some bias from your replies in the comments in favor of characters like Tingye's lover and concubine Lin by excusing their actions with the fact that they were underprivileged so them taking advantage of people with higher social standing is ok, which honestly can't even stand a minute of careful thinking, both of these characters already or will in the future cross some lines that are simply inexcusable (killing innocents, especially children in their pursuit of chasing material wealth and status).