Unable to set up Two-factor Authentication on macOS 10.15

See the article https://support.apple.com/en-in/HT205075

We also recommend that you have a valid credit card on file in your account. This information may be requested to help verify your identity if you forget your password.

While most iCloud users can now turn on two-factor authentication, certain account types may still be ineligible at Apple’s discretion.

Some Apple IDs created in iOS 10.3 or macOS 10.12.4 and later are protected with two-factor authentication by default. In this case, you see that two-factor authentication is already turned on.

See the Apple Support articles below for contact information.  

Apple ID - Official Apple Support.    

Contact Apple for help with Apple ID account security - Apple Support.   (Link doesn’t always load)  

Get Support          Work through the screens to get a chat option. 

Apple Support schedule phone call

https://twitter.com/AppleSupport

See Two-factor authentication for Apple ID https://support.apple.com/en-us/HT204915  See this section especially Setup two-factor authentication for your Apple ID. From this section, "Two-factor authentication is available for Apple ID accounts with at least one device that's using the latest iOS, iPadOS, or macOS. Learn more. You can follow these steps on your iPhone, iPad, or iPod touch to turn on two-factor authentication." 

Note that, even though the latest iOS, iPadOS, or macOS devices are mentioned above, sometimes two-factor authentication is not available. "While most iCloud users can now turn on two-factor authentication, certain account types may still be ineligible at Apple’s discretion." See Availability of two-factor authentication for Apple ID https://support.apple.com/en-us/HT205075

As that thread quotes, some AppleIDs are not eligible. Apple does not elaborate any more on that. You will need to contact Apple about why your AppleID is not showing the option for 2FA.