Good question! The suffix "-iz" denotes the plural by itself, if you think about it. "-iz" signifies "we are." We are fine: iyiyiz. In English, we have no "we" suffix; we only use plural. But in Turkish, the "we" suffix by itself suggests plural. Öğrenciyiz: We are students. I suppose if you wanted to say we are something singular, like "we are one nation," you might need "bir": Biz bir milletiyiz. Native Turks, do I have that last sentence right?
Isn't there an earlier lesson where "bizde" means something like "at our place"? Could you say "Bizde kurban," for "We have the victim," meaning, for example, that the police were looking for the victim, and we found him and have him here with us? (I know that this is not what "Biz de kurbaniz" means.)