A company doesn't legally (atleast in the US), have to accept cancellations by email unless the terms of service( you read and agreed to them) specifically state that you can cancel by email.
What most likely happened is they replied to your emails telling you to call in or use chat, and you didn't get the email. Don't want to have to call or chat? Don't sign up. Read the agreement.
It was your responsibility to follow up and you didn't do it. Grow up and accept it.
