Deauthorizing computers has to be done on a computer (Mac or PC) from inside a specific Apple app (Apple TV app or Apple Music app or iTunes app), while being signed in to this app with the Apple Account as used for authorizing in the first place. [You can’t deauthorize while using a different account than used the authorize previously. It is important that an optional previous Apple Account on that computer has deauthorized the computer before signing in with a different account.]
Not sure if you even can deauthorize from an unauthorized computer. I see logic in only supporting that from an authorized computer. Could that be it?
This (de)authorization procedure is not available through the web.
Authorizing or deauthorizing is about the link between a computer device and an Apple Account. Any Apple account can have up to 5 authorized computers (and up to 10 devices-with-download-capacity linked total when mobile devices are included).
On computers, you can deauthorize just this one computer on which you do this, or deauthorize all computers. You can also see (in Account Settings) how many computers were authorized. You can’t deauthorize a computer that hasn’t been authorized yet.
Please review the following support article for the described procedure, making sure that nothing essential was skipped.
Authorize or deauthorize your computer for Apple Account purchases - Apple Support
Why can't I do this via the website?
While there are probably technical reasons to not offer that, in general Apple doesn’t share their reasons for any decision that they make, so “why”-questions aren’t that useful on this forum.
“Your request produced an error.”
Was that the result notification for the deauthorizing attempt?
as I had to rebuild my laptop
The authorization links a device to an Apple Account. Depending on what type of rebuilding you did, the hardware identifier in Apple’s administration may or may not have changed?
If you need more help, then perhaps someone else can chime in with their view? Else contact the Apple Support staff.