I was recently watching an interview that John Conway did with Numberphile. By the end of the video, Brady Haran asks John: "If you were to come back a hundred years after your death, what problem would you like to know about ?" He replied: " I would really like to know why the Monster Group exists." From what I have read, it seems like research has moved on toward exploring the connections between the monster moonshine conjectures and other fields such as conformal field theory. I do know that Conway didn't particularly like the idea of the existence having to do with CFT (see: https://www.ias.edu/ideas/2013/roberts-monster ). 

Therefore, I am trying to understand what he means by "why" ( I couldn't really find any papers where he further went into the question, why can't the existence of the group be a coincidence ?). Have there been any further developments in relation to this question? 

The interview: https://youtu.be/xOCe5HUObD4