Payment verification

You only get to choose none when you set up a new account. If it wants verification, you will need to enter payment or contact support and have them somehow waive that on the back end.

See:

• Can I download a free app from the App Store without a credit card?
• Do I need a credit card on file to get free apps?

Now - once you've added a card and verified, you might be able to go back to none, but your account was somehow flagged as needing verification so Apple Support would need to weigh in if that was intentional or can be waived.

You may have an outstanding charge made to your account. Call Apple Support (1-800-MY-APPLE) and ask to speak with iTunes Support. They'll be able to take a look at your account.