Special right of cancellation in the case of motor vehicle insurance

I actually wanted to change to a new insurance policy at the turn of the year. I quickly sent off the notice on Monday and made everything possible with the new insurer. now call my current insurance this morning and tell me that I can’t quit so easily. I of course immediately to 180, because I thought “what do they actually make up?”. Then have discussed back and forth why I change and what is better until I say The agent of the new insurance company said that the termination was now legally valid and that I will not shake it any more. Then the clerk says again that I could not terminate because I did not quit within the deadline. I wrote in the notice of termination in a shameful manner, that I quit on 30.11.2004. Of course I should have written in 31.12.2004, but had always only the sending before 30.11.2004 in mind. The agent of the new insurance company said that he wants to re-examine whether I happen to have a special right to cancel the contract or whether I can rely on the fact that, of course, I could only have quit at the end of the year and that the old insurance has no control over me. What do the experts here think about it? We have some real estate agents with us, right?