"Why people shouldn't...."
Don't tell others how to watch drama. If the storyline changes down the road and if the mother warrants a pity party, it's up to the viewers' own judgement. You may hold your judgement on the mother, and you may think you wouldn't blame her too much, but that's you, and that's your way of trying to make sense of her situation. However, don't tell others how to feel. Some viewers may also relate to Tae Sung's feelings, the resentment of being neglected, of not having an adult being there for them during their most difficult times. Don't try to say we should all look at things "objectively" either. Viewers would either take the mother's side or the son's side. It's a personal choice.
Honestly? I find it ridiculous people keep saying "the mom is a big celebrity, she just doesn't have time!! She's just really, really busy, and things just happened!!"
Well, Tae Sung is now also a big celebrity himself. Is he not busy, too? Does he not have a stupid crazy schedule himself? How many years has he been working as a top star now? Six? Eight? But he knows his priorities. He still makes time for Han Byeol. Why? Because he really treasures her and loves her. His mom made a choice. Life is about choices. And if some viewers decided to villainise the mother, they have every right to do so. It's just a damn drama.