I think there's something wrong with your installation, the gem path shouldn't have ruby-2.0.0 in it?

Jazzy does work on Ruby 3.0.0:

; ruby --version
ruby 3.0.0p0 (2020-12-25 revision 95aff21468) [x86_64-darwin20]
; jazzy -h | head -5
Usage: jazzy

Options
    -o, --output FOLDER              Folder to output the HTML docs to
; jazzy --version
jazzy version: 0.13.7
; uname -a
Darwin Johns-MBP 20.5.0 Darwin Kernel Version 20.5.0: Sat May  8 05:10:33 PDT 2021; root:xnu-7195.121.3~9/RELEASE_X86_64 x86_64

😂I tried to install it and then it showed it is successful.

I mean that your Ruby installation looks confused: study the info you posted above, it is mixing up the system Ruby 3.0.0 in /usr/local/lib with an RVM Ruby 2.0.0 in ~/.rvm.

I'm not sure it helps your problem, but it looks like there is a change we need to make for rexml in Ruby 3 - https://stackoverflow.com/questions/65479863/rails-6-1-ruby-3-0-0-tests-error-as-they-cannot-load-rexml.

For now you could install rexml manually or use Ruby 2.6/7.

@johnfairh I will try and then ensure the issue, but it's so weird........The same action occured on two machines, but only one has problem.

The solution as blow:
gem install rexml

and then all is okay..

Keeping open to remind me to update the gemspec to include rexml as part of Ruby 2.6 requirement.

Fixed by #1264 in master.