Drush uses --defaults-extra-file which is overrided by users .my.cnf

[jkolkka]

Drush uses --defaults-extra-file when connecting to database for storing username&password. If current user has .my.cnf in his/her home folder it will override --defaults-extra-file.

Example:
settings.php found in sites/default

$databases = array (
  'default' =>
  array (
    'default' =>
    array (
      'database' => 'dev_base',
      'username' => 'dev_user',
      'password' => 'dev_password',
      'host' => 'localhost',
      'port' => '',
      'driver' => 'mysql',
      'prefix' => '',
    ),
  ),
);

~/.my.cnf

[client]
user="my_user"
password="my_password"

When connecting to MySQL drush will create tmp file with following context:

#This file was written by Drush's Sqlmysql.inc.
[client]
user="dev_user"
password="dev_password"

And it uses it like:
mysql --defaults-extra-file=<previously created tmp file> --database=dev_base --host=localhost --silent

Because .my.cnf overrides --defaults-extra-file previous command will try to connect with user my_user and if my_user doesn't have permissions to access database drush will fail to connect to database.

[weitzman]

Honoring my.cnf is by design. If you dont want it, delete that file.

[minerva-atrix]

This is not a good enough answer. Scripts on the server setups I have already use .my.cnf for doing a lot of tasks. Drupal's database is on another machine. Drush needs a way to disable this functionality and it's bad it was ever added. It's been very disruptive see:
https://www.drupal.org/project/drush/issues/2852233
#2750
#2183