Cancellation by contradiction

If I owed you five bucks,
And you owed me five bucks too,
What does it amount to? A cancelled out flat position.

If you push from the other side,
And I push equally from the side here,
What could it possibly lead to? A cancellation of the two forces.

So, if it works in accounting and works again in physics,
The big question here is does cancellation by contradiction work in the human mind too?
If a wishful impulse is driving me insane to do immediately an activity A,
Could I hope to preserve the serenity of my mind by injecting the contradictory thought of NOT wanting to do A?
As most would say from their personal experiences, far from cancelling out each other, both the impulses now hold the mind for ransom – where previously there was just one.

So, why do thoughts which are mutually contradictory make no attempt to do away with each other?
Why do contrary impulses exist side by side, without cancelling each other and vanishing from the ecosystem of mind?
Wanting to do a thing or not wanting to do the same thing, or wanting to do two different things – each of which is completely at odds with each other, none of the impulses in the mind diminish each other or cancel each other out, but only combine together to walk some middle path – the big compromise.