Why do only certain websites require an extra 3-D Secure authentication step during online payments?

3-D Secure is an added security feature that you can opt for (if offered by) your Payment Service provider. You can opt to have it turned on or not, this depends on your type of exposure you will allow yourself to be subjected to, the financial regulations in your country and also the underwriting terms & conditions by the acquiring bank and/or PSP.

In short, its not that you have to use it, but it greatly reduces fraud and the onus of the fraud goes to the acquiring bank rather than the merchant.