If an insurance cancells you, why would they want you to file a cancellation after the fact?

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Paid for a one year policy for my home incurance in November 2010. The policy was to take effect on December 20, 2010. Prior of the policy taking effect the company sent their inspectors and pictures were taken of the home on a second visit. The policy took effect and I was happy to have my home covered. The first week of February 2011, I received a letter informing me that "a temporary wooden building" used only for storage and already told the company it was coming down as soon as it was possible for me to do so. I'm elderly, disabled and leave alone in the County with a fixed income. I responded saying that I would take care of it as soon as I could (lots of rain and winds at the time). They then asked how long did I think it would take to get it down. I said as soon as the weather permitted it and could get help in doing so! I was then told that my policy was cancelled as of March 11, 2011. I responded and told them that if they already cancelled me after saying they wold give me time to take care of the problem that was bothering me more then it did them, then I wanted it cancelled on February 20, 2011 at exactly two months since issuance.
Then they said, I would have to send them a form requesting cancellation; minwhile by February 20th, 2011 I had taken the building down and paid for a container to take away. Pictures were furnished to prove what I said to them. I also told them that it was incredible that they cancelled me out and asked me to write and send a cancellation. To booth they referred to my dwelling as being in poor condition etc. etc. I told them I wanted that off my records. No I did not send them a form, but only an e-mail and a fax telling them again that since they cancelled me already, to make the cancellation effective the 20th of February. Their response came today and still they are trying to say that I did not send them a cancellation. I have their form letter cancelling me already.
What game are they playing anyway? I'm put in a bind so now I cannot shop elsewhere as I don't have the funds until I get my refund and their documentation corrected. I abide by the rules and did my part. I entered this contract in good faith and I got the shaft. I've never been cancelle before by an insurance company. Please advice. This poor old lady needs help.
Thank you.