Poor you your family!!!
Maybe you are the product of a mixture between a white and a yellow Vietnamese who does not want to accept his origin. Therefore, he has taught you by his way: given you a mess of bad information about my culture, Vietnamese culture I mean.
As Paddy words, people rarely find out a Vietnamese person who doesn’t know exactly about his/her birthday as well his/ her zodiac sign although he/she comes from the rural area or downtown. Moreover, if you ask a little girl/ boy, she/ he can tell you very clearly about her/his birthday in Solar or Lunar.
What a pity when you have a haft of Vietnamese blood in your body but you know nothing about your haft origin culture.