Square circles do not exist. Proof = Squares have corners, circles do not, therefore a square circle does not exist.

Just proved a negative.

The claim that you can't prove a negative is incorrect. The claim should actually be that you shouldn't try to prove a negative. This is reasoning to not CLAIM a negative, not to claim all the negatives you want simply because there's no way to prove it.

One should not make claims that they cannot prove. Absence of evidence is not evidence of absence. Isn't that what the religious say all the time? Does an atheist have to prove there's no god to make the claim that there's no god?

The court rules the person "not guilty", because they cannot demonstrate that the person is innocent. The court has to prove you guilty, your defense does not have to prove your innocence.

It's up to any person to prove their claim. One person claims there's a plan, another person claims there's not. Each one of them could be wrong.

If you say, "There is no plan", that is a statement that could be incorrect. Since it could be incorrect, then you have a burden of proof. It is not just ASSUMED to be correct.