Maybe because Taesung is seen as a popular person, and Haebom isn't a very sociable person, it wouldn't make much sense that they live together. Especially since they started drifting away from each other due to a misunderstanding. Also it could be because of Haebom avoiding (unconsciously) Taesung and not knowing what to do with himself other than make himself go unnoticed. ┑( ̄Д  ̄)┍
Tbh, i dont get why he has to hide the fact they they're living together. But we have to put ourselves in haebom's shoes. He's practically freeloading his mom's friend. Someone who doesn't have any relations with him. If it goes out that he lives with taesung, those rude people would probably mock him. Besides, he has low self confidence and he also thought that Taesung hates him.
Then, are they more like his temporary legal guardians or something?
I'm just wondering why they have to hide the fact that they live together? Is it to avoid rumors about haebom being adopted to taesung's family?