Why can’t I use an array of term slugs in WP_Query?

If you read the codex page carefully, you will see that taxonomy parameter {tax} (in your case it is customtaxonomy) takes only string value. Furthermore such taxonomy parameter is deprecated from version 3.1. So in your case you have to pass tax_query array with terms array:

$query = new WP_Query ( array(  
    'tax_query' => array( 
        'terms' => array( 'term1', 'term2' )
    )
) );