As a native of South Korea, it is perplexing to understand why Canada is still under a British monarch. Can you please explain ?

Canada is not under a British Monarch, Queen Elizabeth is a Canadian Citizen and her family was chosen by the Canadian people to be the Royal Family of Canada through their elected representatives.

it is just a figurehead. a bit like the bald eagle is the symbol of USA.

I could explain but tl:dr

if it isn't broken why fix it.

"British monarch"

She is a Canadian citizen, thats the crucial but that trips you people up, its fun watching your heads explode.

Canada is an independent country, part of the Commonwealth alliance. The nominal head of the alliance is the Queen.

We aren't, and haven't been since the Statute of Westminster in 1931.  The then "British" monarch's role was separated, one for each dominion.  Thus, Elizabeth II is "Queen of Canada."  She might be Queen of other places as well, but, we don't care, and the other roles are legally distinct, and operate under different laws.  HM is the Head of State for 16 different countries. 

Canada gets a real bargain; we cover certain expenses when she visit, as well as the Governor General, etc., (costing about $1.50 per person, per year), but we don't actually pay her at all for the work that she does.  Which is a good reason to not change the system - it works well, and it is free!

It's a nominal position. The Queen has no powers over Canada. Canada operates as an independent country with the Queen as a figurehead. 

Wikipedia says GB (the British Monarchy) has ongoing relations with 171 of the 193 countries in the UN. You saw what happened when the Falklands tried to disengage themselves from GB. THAT'S why...