There is an error coming in my site when I am subscribing with email from Newsletter subscription form.
I have checked in admin panel also, the email is not present in Newsletter subscription list.
Please check whether you have same email registered as customer or not.
I think Magento checks in customers table apart from newsletter subscribers table when a user tries to subscribe to newsletter from global newsletter subscription form.
When an email address already exists in customer table as a customer, Magento does not allow email address to subscribe for newsletter from global form. Instead, registered user can manage newsletter subscription from his account panel.
I hope, I was clear enough to answer your question.
Please let me know in case of any confusion or query.