Here's a simple example:
I state this to be true:
If it is raining, I am wearing blue socks.
If I am wearing blue socks, you cannot conclude that it is raining because I did not state that blue socks are worn only when it is raining.
The above is not an example of the law of noncontradiction, nor is it an example of a contradiction. But it is an example of a logical fallacy. (The name of the fallacy is affirming the consequent. --LMS