Uhm... Here's some Spoilers?
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It was actually NianNian who begged the mom not to say it (and the mom promised NianNian so ╮(￣▽￣)╭). NianNian wanted to keep it a secret from Yansheng, because he wanted Yansheng to truly fall in love with him. He doesn't want to use Yansheng's guilt as a bargaining chip to return his feelings. (In contrast of what the fake savior is doing, which is taking advantage of Yansheng's gratitude and guilt).
But if I were Gu Yansheng's Mom. I will tell him. He has a nerve of hurting the who saves him. Because of him, Nian Nian suffered so much. Then he will believe that cunt's lies. Unbelievable
She's a plot device (´；ω；`) she's just doing her job to add more drama aight. Sometimes I just really had to give up logic for this kind of stories and just go with the ride (╯•﹏•╰).
Why won't the mom just let them tell yansheng that niannian was the one who saved him??? Let's make him suffer more plis.