"Are you 'Han'?"

"So are you 'Han'?" My Colombian classmate was very curious. I hadn't given much thought to it until I came across this question right in the face. 

Han dynesty (206 BC–220 AD), was when old "Chinese" (as known in the Western world) or, more precisely, Han characters (also known as Kanji in Japan & Kanja in Korea as "sister systems") were standardized. The first dictionary of Han characters《說文解字》published in 120 AD, explaining the six principles of Han character formation (六書), is still being taught at schools in Hong Kong.

The use of the ancient scripts is in many levels different from the "traditional Chinese characters" adopted in Hong Kong and Taiwan nowadays (in the sense that I can technically read the old characters without understanding anything), let alone the Simplified ones (formed in 1956 AD) in the PRC and the pronunciations of the characters.

For me, therefore, the answer to "Am I Han?" doesn't really matter. If one had to categorize himself Han because he uses Han scripts, many white people would have to refer themselves as Latin/Roman (although many Portugueses and Hispanics do, but that's another story). Language is a carrier of culture, but it forms only part of one's identity.
By the way, "Hanzi" is Mandarin, "Honji", however, is Cantonese.