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Ok now this is starting to really come together. Taekyung has done all of this not just to keep his promise to Heeseo's mom, but to protect Heeseo from the accomplice who probably killed the mom and tried to kill Heeseo too,... is what I'm getting from today's chapter.
That makes a lot more sense as to why he won't say anything to Heeseo and why he's been so obsessed with finding out what really happened. I have a feeling that since the prosecutor who took the letter is a woman, she may be the accomplice or know them. That would make sense as to why the Mom was so afraid of them and didn't want to get anyone else involved.
I wonder if Taekyung said something to the wrong person back then, trying to help the mom and somehow it got back to the killer.
These are all just my theories based on everything up to now.