Wen, I would concur with your tutor that reading the bible will give you insight into western culture.
Many here who have no time for the bible will say it doesn't, yet much of our values, laws, and how we view the world are loosely based on it.
That said, much of our values, laws, and how we view the world have other sources of influence as well, so don't take the bible as any where near authoritative on western culture.
Only the new testament is relevant (as far as I can make out). And I would skip the book of revelations, which doesn't affect the culture at all, except for people being paranoid about the number 666, and armageddon, oh, and hell...well, damned, I guess it does have some effect on our culture.