As we all might know that today is "Safe Internet Day". So Google is reminding us for the security check-up. I tried it. And I saw that I could remove my security question. I did it with the belief that I will add a better question (I forgot the answer of the earlier question anyway).
But when I tried it then I found that there is no option to add a new security question. I believe that the security question is necessary. Here is a picture how Recovery options looks like for me.
There should be something with the name called 'Security Question' below 'Recovery phone'. Is there a way by which I can add that question? When I removed it I even got a mail from Google. By clicking that link I was directly forwarded to 'My last device activity', which is definitely not helpful in adding the question again.
Best Answer
Google found that security questions were not really secure at all as most of the answers can be found with a simple Google search. For example Sarah Palin had her Yahoo! account hacked because someone simply Googled her birthday, ZIP code and where she met her spouse.
Google has completely removed support for security questions and one only had the ability to remove already existing ones. There is no way to add your security question back in.
Perhaps you should consider enabling 2 - step verification, enabling this feature will make Google send a single-use code to your phone which you will have to enter as a second password. In this way even if someone manages to acquire your password, they will also need your phone to access your Google account.
Please also read: How to create a secure password.