Reset the security questions.

I also have this problem, and cannot enable 2FA because I don't know the security question answers (I have no memory of ever setting them up, in fact).
Originally I needed to know an answer to a security question to reset the security questions as above (What? Seriously, what?Did anyone think that one through?)

Then I reset my password in the hope that would help, and now if I try resetting the questions I get 'Cannot Reset Security Questions - We don’t have sufficient information to reset your security questions'. So don't do this. It doesn't help. You might even say it hinders.

Much as I'd love to take this up with normal Apple Support, that just routes me back to the broken page over and over again.
There's no phone, no email, no nothing apart from 'go to this broken page'. So, now I can't release or manage any apps. Oddly I can still build and submit them via Xcode though!

What's the way out of this?

I also have the exact same problem ... can't access my apps, very annoying. Weirdest thing ever since I did not loose my password and I can still log in to some parts of apple.

I also have this problem. It asks me answer to security question for resetting my security question!!! what the hell?!! Any workarounds ?

I was able to overcome this by signing into my iPhone with the developer account details (Apple ID), then next time I tried to login it automatically enabled the 2FA and skipped the security question.