Bash: duplicate + rename folder

Tutorial copy files, folder link: link

Manual cp command : Link

cp -frp /path/to/folder/my_folder_old -T /path/to/folder/my_folder_new

   -f, --force
          if an existing destination file cannot be opened, remove it
          and try again (this option is ignored when the -n option is
          also used)
   -p     same as --preserve=mode,ownership,timestamps
   -R, -r, --recursive
          copy directories recursively
   -T, --no-target-directory
          treat DEST as a normal file

Though if my_folder_new already exists, my_folder_old is created inside the first and not substituted. Why is this happening?

The reason why is this happening because, my_folder_new already created. Doing same cp command it will see as new path, /path/to/folder/my_folder_new/