someone has to forget person, so that they can still live i guess‽

Not rlly, it was just yeon's choice to make kihoon forget him since all of kihoons misfortune in their second life happened because of him(well more of bc of the rock but still bc of him indirectly) so yeon thought this time kihoon should live for himself without fear of losing someone/something he loves(on s1) and he did? Or he is, technically