The problem is in the file assets/plugins/tinymce/tinymce.functions.php. This file sets some of the configuration for TinyMCE, including the plugins and buttons for the various types.
For example
case 'editor':
$plugins = 'autosave,save,advlist,clearfloat,style,fullscreen,advimage,paste,advlink,media,contextmenu,table';
$buttons1 = 'undo,redo,|,bold,forecolor,backcolor,strikethrough,formatselect,fontsizeselect,pastetext,pasteword,code,|,fullscreen,help';
$buttons2 = 'image,media,link,unlink,anchor,|,justifyleft,justifycenter,justifyright,clearfloat,|,bullist,numlist,|,blockquote,outdent,indent,|,table,hr,|,styleprops,removeformat';
$buttons3 = '';
$buttons4 = '';
break;
As you can see, no italic button. The first several cases don’t have it, while the last three do.