My roommate and I emailed our landlord in DC asking for a one month extension. He agreed but did not list the price of the apartment, etc.
You asked for a one month extension, he agreed. Very generous of him. Listing the price was not necessary, unless the price drastically changed. You don't mention that. So, did you pay more for that one month extension?
then we both found new places that were closer to our original lease date, so we emailed and asked if we could move out on the date that was in our lease. He said no
You can ask, but since you had already extracted an agreement to stay a month beyond your lease, from your landlord, you had a pre-existing agreement with him, and he has every right to say no to another new agreement. He doesn't have to go by your whims. You asked for the extension of a month, he allowed it, now, because your life is suddenly good and you found a new place, you expect him to swallow the money for that month he agreed to that he didn't have to? The month you asked for when you thought you needed it, but now want to dismiss because you no longer need it? Think about it. Is that fair?
is an email binding if we did not sign anything
You expected it to be binding, right? When you asked and he said yes, you expected him to go by his word, his word by email. But now that it's no longer to your benefit you don't think it's binding? It's binding. As binding as you expected it to be when you asked for it to begin with.
My roommate was also the one that emailed so my name was not attached to the original email.
Is your name on the lease? If so, that email spoke for both of you.
Just pay the months rent you asked for!
My roommate was also the one that emailed so my name was not attached to the original email.