Why is "positive" chosen as the opposite of "normative", as in "positive statement"?
This is the oldest sense of the word positive, deriving from classical logic and rhetoric. A positive statement is one which posits a fact, from pono, literally "to place"; compare proposition, an assertion which is "placed" before you for your consideration. A positive statement asserts a fact to be true, while a negative statement, from nego, "deny", denies its truth.
Positive and negative have acquired further senses since these words originally entered the language, but in speaking of the logical meaning of statements these meanings still apply.