I select "pay with federal refund" then press continue and I am brought back to the same page and the "pay with federal refund" option is gone. What is going on?

If you're receiving a Refund in an amount sufficient to pay your TurboTax fees, you should be able to 'pay with Federal Refund' in the FILE section.

If you're using TurboTax Online, close the program, clear your Cache and Cookies and return to the FILE section.

Here's more info on How to Change Refund Method.