It is not easy .Ml doesn't have any memories of them dating So how could he believe her at first.Also don't forget ml's mom hates her and she knows that that She doesn't even know if his family will accept her and daughter .So in this situation everyone would try to hide it And she doesn't hide it from everyone
In Korean culture it's looked down upon highly to be a single parent, kids get bullied raped etc because of it in schools too. She also put down single on her resume so it would be lying on an official document or effectively lying in work culture about your home life. And yes KOREANS CAN BE VERY NOSY not all of them but especially those that work in a corporation. Plus if she said the father left or she was never married a Korean woman would be sexually harassed for "opening her legs" which depending on the work culture would lead to sexual assault. It's a whole bunch of bullshit but it is what it is
im actually pissed off she couldve told them it was her daughter's birthday or something rather then trying to keep it as a secret... even if it was for the plot it just felt like her being a good mother was less important compared to keeping her child a secret from her boss