So your ideal society is one in which people get killed by "Professionals with black clothing and silenced weapons" hired by anyone who thinks they are cruel to animals.
It is not ideal society, it is society that may be better than what we have now, or at least not worse,
since we have people which get killed by professionals with blue clothing, called on by anyone who thinks they are cruel to animals. Besides, it not necessary to kill. Give very stern warning to these people, maybe with warning shots, and it may be enough to give them notice that they are being watched. This is not so much possible with just calling police who may just come, investigate, and leave if they can't come into house to investigate.
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If your idea of anarchy is worthwhile, it has to offer something better than what we have now in our real lives. You offer a society in which "Professionals with black clothing and silenced weapons" are killing people for animal cruelty and then seek to justify that by arguing its exactly how things work now.
You can prove any point if you make things up. Why not compare your "Professionals with black clothing and silenced weapons" instant execution system with the real world in which a death sentence requires a jury and years of careful examination of the facts? Your idea is certain to involve a lot more people being killed.
Try to look at the logic of
http://en.wikipedia.org/wiki/Separation_of_powersAny decent society will have a clear separation between the judicial act of deciding to kill someone and the executive act of killing them. "Professionals with black clothing and silenced weapons" type systems where private individuals select victims and have them killed breach this principle. That's tyranny - not freedom.