How do I get iCloud Two-Factor Authentication to work? (cannot turn on to begin using)

I click 'Continue', then 'Continue' for the 'Turn On' Radio button, a loading icon rotates for several seconds, then I'm back at step 1 and nothing appears to have happened. Is bluetooth tethering 4G too slow an Internet connection for this feature to function? Is there a server connection problem so that I must use a different Internet connection? What is the problem? Two days ago, on Wi-Fi, I tried and instead was getting a six digit code to enter, but despite entering it properly, was told to try entering it again. Both SMS and phone call six-digit code gave the same error, 'try entering it again'. Now I'm not even getting to that step. What is the problem? What is the solution?