ARC for TW/Canadian student

I arrived to Taiwan last week as exchange student at National Taiwan Normal University. Before to come Taiwan, I applied for resident visa at TECO Canada and they sent me back my Canadian passport with Taiwanese visa inside. Since I study two semesters (September 1st to June 30 2016), I need to apply for ARC. I entered in Taiwan with my Canadian passport. I know I’m dual citizen, a TECO employee told me that a year ago. Today I went to National Immigration Agency for ARC, but the woman worker saw my birth place is Taiwan. She asked me if I have household registration which I didn’t know since I was adopted by Canadian family at one year old. I showed her a picture of my old ROC passport as a baby and she explained to go household registration office and show them my ID number of the passport. I need to have household registration transcript. A Taiwanese friend of mine doesn’t understand why I need that paper for ARC. So can I apply for National ROC ID card?