Unable to change Apple ID security questions due to insufficient information

Try this

Reset your security questions

1. Go to iforgot.apple.com.
2. Enter your Apple ID, then select Continue.
3. Choose the option to reset your security questions, then select Continue.
4. Enter your Apple ID password, then select Continue. 
5. Follow the onscreen steps to verify your identity. The information you’re asked to provide may vary based on your account details and other factors. If you don't get any options to verify your identity, you can't reset your security questions at this time.
6. Choose new security questions and answers and select Continue. See our tips for choosing security questions and keeping your account secure. 

After you reset your security questions, you might want to set up two-factor authentication instead. It's the best way to keep your account secure, and you won't need to remember any security questions. You can set up two-factor authentication right from your iPhone, iPad, or iPod touch with iOS 9 or later or your Mac with OS X El Capitan or later.

After you have. Changed your security questions, make sure to update to 2 factor authentication instead of 2 step authentication with security questions, as this is no longer supported by Apple

I see that an earlier reply missed the part where you say you are getting the 'not enough information" message.

Several years ago Apple transitioned to using two factor authentication instead of security questions. You can continue to use security questions if you already use them and they are working for you, but if you have problems then they no longer get direct support. You can try the directions in this support article If you forgot the answers to your Apple ID security questions - Apple Support but the article is labeled "archived" and may contain information that no longer applies. If the instructions work then fine; if they do not (e.g., you see “not enough information”*) then you will have no option but to change to the newer security method, if you can. Over the past few years Apple has been persistently encouraging users to switch to the newer two factor authentication security system. For those who have disregarded their encouraging, Apple will likely only help you to now change to two factor authentication, if even that is possible. Follow the instructions in the "Turn on two-factor authentication for your Apple ID" section in this support article --> Two-factor authentication for Apple Account - Apple Support to try to change to two factor authentication.

If you still need help, contact Apple Account support at this link ➞ https://getsupport.apple.com/?caller=cups&PGF=PGF63005

Select "Other Apple Account Topics", then "Security concerns or account compromised." This will give you a chat or telephone call option.

If Apple cannot, or will not, help you transition to two factor authentication then it is quite possible you will have to simply abandon the old account and everything it contained. In that case, if you were using the Find My service, the Activation Lock support request support article at: - https://al-support.apple.com/#/additional-support may at least let you regain use of your equipment. If not, you will also have to say goodbye to that as well.

Good luck!

*See the third page of this discussion Unable to Reset Apple ID Security Questio… - Apple Community Some people talk about getting out of a “loop” by logging in a different way. I am not really following what they are talking about but maybe you can see if it helps.