You are running with php 5.3 or earlier. Drush 8 needs php 5.4 or later. Unfortunately, php 5.3 does not understand array syntax, so the failure is raised before any Drush code runs. For other sorts of errors, Drush will tell you that your php is too old.
I am guessing you are using php 5.5 for Drupal 8; check
which php and
php --version to see if your php-cli is the same version as your Web server php.
Set the environment variable DRUSH_PHP to the full path of the PHP executable that you would like to run. Note that this will only work if you are using a Composer or git install of Drush; if you are using drush.phar, this feature is not available. For the .phar, you would need to use a shell script named "php" that calls php5.6. Then, set your PATH such that your php script comes before the one offered by default on the platform.