I want to delete Apple ID, but I cannot reset security question.

See -> If you forgot the answers to your Apple ID security questions

If you forgot the answers to your Apple ID security questions - Apple Support

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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.

If you answer your security questions incorrectly too many times in a row, you temporarily can't use your security questions. Try to reset your questions after the waiting period ends.

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I want to delete Apple ID

If you have deleted it, it is no longer valid, it simply no longer exists and it no longer works.

To understand about a deleted Apple ID, see the Apple articles below:

How to delete your Apple ID account

How to delete your Apple ID account – Apple Support (UK)

Understand and control the personal information that you store with Apple

Understand and control the personal information that you store with Apple - Apple Support

Hello,

Try the directions in the article If you forgot the answers to your Apple ID security questions - Apple Support for resetting your security questions:

"Reset your security questions

1. Go to https://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."

If you get a message about not having 'sufficient information', you will not be able to reset your security questions.* Realize that several years ago Apple transitioned to using to two factor authentication instead of security questions and has been encouraging users to switch to the newer security system. Your next recourse will be try to change to two factor authentication as outlined in this article --> Two-factor authentication for Apple ID - Apple Support Follow the instructions in the section "Turn on two-factor authentication for your Apple ID"

If you wish to speak with Apple about this, contact with Apple ID account security using the information in this document --> Contact Apple for help with Apple ID account security - Apple Support

If you do manage to get the account working again, have a look at How to delete your Apple ID account - Apple Support

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*Dec. 2022 post by Apple Community Specialist K_Faith in the thread I’ve tried resetting my security question… - Apple Community

"If you’ve forgotten your security questions, there isn’t a way for Apple to reset them for you, or another way to access your account. You would need to create a new Apple ID, which also means you won’t have access to previous purchases or data stored in iCloud."

In regard to what the Community Specialist said, deleting the account may be moot. It exists but you can't do anything about it and neither can anybody else. Eventually: Legal - iCloud - Apple

VII. B "In addition, Apple may terminate your Account upon 30 days’ prior notice via email to the address associated with your Account if (a) your Account has been inactive for one (1) year; or (b) there is a general discontinuance of the Service or any part thereof."