Apple is simply trying to make it easier to purchase apps if you decide to do that in the future. Providing the security code on the card lowers the fees Apple pays to the credit card processing company since it is evidence you are in physical possession of the card.
You aren't required to provide a credit card at all just to sign up. When you are prompted for the credit card type, Apple gives the option to chose "None". If you choose this while purchasing a free app, it will allow you to sign up without a credit card.
Apple provides walkthrough steps for doing this on both a computer and on an iPod touch or iPhone.
If this method is not available in your country but your country does have iTunes Store gift cards available, you can purchase one gift card and use it to create an account. You'll have to pay a little up front of course, but you won't have to provide a credit card before starting to purchase the free apps.