In order for there to be anarchy, there must be no rights...

Yet again, this is complete and total bullshit, and destructive bullshit at that.

You're everything that's wrong with anarchism. If you had your way about it, society would be reduced to raw brutality, in which, with nobody ceding any rights to anyone else, everything would just come down to who was most willing and able to kill other people. That's not going to lead to stable anarchism - it's going to lead to despotism, as the most ruthless and vicious inevitably come to dominate and all others are forced to submit.

Luckily enough though, it's relatively unlikely that your destructive bullshit would take any sort of hold in a stable anarchism, because other people would likely recognize you for the sociopath you so obviously are and would refuse to interact with you at all. It certainly wouldn't take them long to recognize, as I have, that you have no respect or consideration for other people - that you view them as nothing more than objects to be used however you might see fit, constrained only by the threat of consequences to yourself, and thus could never be trusted. At the very least then, they're going to shun you, as someone who clearly can never be trusted.

Meanwhile, healthy and rational people will be choosing to respect the rights of others, and will be building a network of like-minded people, each and all knowing that they can trust each other - that just as they willingly cede rights to others, other willingly cede rights to them.