Setting a preselected option on a select tag requires you to put a selected attribute on the selected option.

<select style="margin-left:25px;">
<?php
   $options = array(array("null"," "),array("single","Single"),array("in_a_relationship","In a relationship"),array("engaged","Engaged"),array("married","Married"),array("open_rel","In an open relationship"),array("divorced","Divorced"));
   foreach ($option in $options){
       if ($option[0] == $row3['status']){
           $selected = 'selected ';
       }
       else{
           $selected = '';
       }
       echo '<option '.$selected.'value="'.htmlspecialchars($option[0]).'">'.htmlspecialchars($option[1]).'</option>';
   } 
?>
 </select>

The solution of Musa it's OK, but If you don't want to change your PHP too much you can do the task with Javascript.

With jQuery or pure Javascript

function selector(id, value){
    select = document.getElementById(id);
  for(i=0;i<select.options.length;i++){
    if(select.options[i].value == value){
        select.selectedIndex = i;
    }
  }

}
//Pure Javascript
selector("status", "engaged")

//With jQuery
jQuery('#status').val('married');

Check this Snippet