I have ext-fileinfo but Composer says it is missing

Windows users: just edit php.ini and uncomment this line:

extension=php_fileinfo.dll

Remember to restart Apache for new php.ini to take effect.

Apparently it is because there are separate php.ini files for web/apache and CLI and as composer uses the CLI and phpinfo() uses the main php.ini the problem occurs.

If you run php -m in CLI and don't see the module's name you should find the CLI php.ini (in my case php-cli.ini and add the extension. e.g. extension=php_fileinfo.dll

I have the same problem. Fixed now.
you can also uncomment this line

extension=php_fileinfo.dll  

in the following files:

1. php.ini-development
2. php.ini-production

Please don't forget to restart your Apache.
Hope this will help.