Update your form to include the term-id, instead of just <input type="checkbox" /> use <input type="checkbox" name="taxonomy_id[]" value="'. $industryterm->term_id .'" />. That way you are actually sending along some values, in this case the term id.
And in the args for wp_insert_post() make sure to include something like this:
'tax_input' => array(
'industries' => $_REQUEST['taxonomy_id']
)