Apple can only send the email to your Apple ID email address or an email address that you had previously set up as a Recovery Contact. It would be a security failure if a person were able to provide a different email address to send the unlock to when they have forgot their password. That is how they know they are sending the information to the correct person and keeps other people from being able to access your account. I would be able to reset your password by providing my email address and you would be locked out of your own account.
I don't recommend using the iCloud address as your Apple ID because of the reason you have encountered, but if you do, then setting up the Recovery Contact in advance is essential in case you forget your password. In addition, since you are asked to answer security questions, it does not appear you have two factor authentication turned on. With 2FA, you can also reset the password from another Trusted Device or from a message send to a Trusted Phone number that you have previously set up.
Set up an account recovery contact - Apple Support
Two-factor authentication for Apple Account - Apple Support
Without 2FA, the security questions must be answered exactly how you entered them when they were set up. Apple is not going to review the answers you provide and make a determination if the answer appears close or not. That is how data breaches occur. It is simply a match from a previously entered field such as birth city where the spelling, including spaces and accents must be exact. Upper or lower case letters do not need to match.
