How do I delete my Xbox Account

You can't delete your gamertag, you can only change the name but there is a fee associated with that if you change it beyond the one free change you get when you make a gamertag.

You cannot "delete" an Xbox account. You can change the WLID to free it up (forums.xbox.com/.../19163.aspx), change your GT to free that up, delete it from your
console, and call phone support (support.xbox.com/.../contact-us.aspx) to turn off auto-renewal if you have a current LIVE subscription.

Why not just change your email address. Here's a link on how to do that:

support.xbox.com/.../manage-live-id

This is total bullshit, microsoft is using us for free marketing, and invading our privacy by not deleting an account when requested. If you log out of your account on the console then start it up, microsoft still records what the console is doing!!

Microsoft need to cut the big brother crap and follow accepted procedures for privacy, why the hell have a phone support centre with option 1 "delete your account" only to be told it cannot be deleted and there is no management staff or anyone with any authority
whatsoever to talk to. Most of us are adults, Microsoft you are on thin ice with your invasive attitude.

There is a method to completely close out an MS account.

Log in to your Microsoft account.

go to security and privacy select more security settings. Click "Close your account".

I suggest you review what it means to completely close out the account prior to doing this.