Wordpress：FORM标签不会仅显示在Admin Post Lists的第一篇文章中

I'm trying to add the FORM tag in each post at Admin Post Lists but doesn't show only at 1st post.

functions.php code for testing

function manage_posts_columns($columns) {
    $columns['status'] = "form test";
    return $columns;
}

function add_column($column_name, $post_id) {
    echo '<form><input type="text" name="mail" size="3" value="" /></form>';
}
add_filter( 'manage_posts_columns', 'manage_posts_columns' );
add_action( 'manage_posts_custom_column', 'add_column', 10, 2 );

1st line source at Admin Post Lists There's no form tag.

<td class="status column-status" data-colname="form test">
    <input type="text" name="mail" size="3" value="">
</td>

After 2nd line

<td class="status column-status" data-colname="form test">
    <form>
        <input type="text" name="mail" size="3" value="">
    </form>
</td>

Is there something I'm missing?

Thanks in advance for any help.

Regards,

The reason is nest form tag.

Admin Post Lists is huge form and I added form tag. That's why it didn't work.