Remember, PHP is a server technology. It isn't intended to make dynamic page content from the client side. For that, you want Javascript (or some other client-side scripting language). (NOTE: You can use PHP, but it will require submitting the page to itself and checking to see if the user has clicked the "add option" button (or whatever). This is very inefficient and requires the user to wait for the page to reload.)
There are a number of good sites out there with information on creating form controls dynamically using Javascript. Do a Google search and you'll be innundated. The following is just a forum post from Bytes, but it is a simple example that you might be able to follow: http://bytes.com/topic/javascript/answers/90868-how-create-check-box-select-tag
