It comes from saying that if God can do anything, then he can be two contradictory things at the same time.
For example, I couldn't be both married and also single. I couldn't be a mother if I had never been pregnant.
And yet, if I was omnipotent, then any sentence that began "I can't..." could never apply to me. If I am omnipotent, then I must be able to do ALL things. And yet, there are many things, like my above examples, that contradict each other. If I was omnipotent, then I should be able to do all things, I should be able to be both single AND married. And that's not logically possible.
Here's another way of looking at it.
Premise: All grown women in my household are married.
Premise: I am not married.
Now, assuming that both premises are true, it is not possible to reach the conclusion that I am a woman, because if I was a woman, I must be married (as shown by premise 1), which contradicts premise 1.
In fact the only possible conclusion that can be reached from the above premises is that I am not a woman. Since I am a woman, then one of the premises must be flawed (in this case, it is premise 2, as I am married).