Yes of course, you are free to do it yourself, but it is assumed on the large scale that that even including retaliations (which are crimes), crime rates would go down. And in a society with no punishments would it be rational to do that? (Given that the friends or relatives of that guy could come after you for coming after him for coming after you and so on..?
It's hard to reason about your hypothetical, because it seems to directly contradict actual experience. But it seems fairly straightforward to reason about what I, personally, would do: I want the chance of crimes against me minimised, so I accept the no-laws state as the best way of getting that. But if I nonetheless am among the unlucky ones, then I want revenge, so I get revenge. By hypothesis, the chance that the other guy's friends will successfully punish me has got to be small, because we've established that crime is very low in this hypothetical universe.
Here is a thought experiment for you. There will be some bold assumptions here, and they may be regarded unrealistic. I am aware of that and the purpose of this query is not to propose some truths about society in general, but to isolate certain characteristics of preferences regarding the societal institutions of law enforcement and punishment.
Assume that there existed a highly trustworthy model that showed beyond reasonable doubt that crime rates anti-correlated with harshness of punishments imposed on criminals. So basically, if policies changed towards shorter sentences, lower fines and lighter penalties, the number of criminal acts decreased (in every category).
Further assume that this was empirically tested and each time penalties went down, fewer and fewer crimes was committed. But the dependence was not linear so if we would get rid of punishments all together - there would still be murders, rapes, robberies etc. But, the crime rates would be minimized in that case. To summarize: We knew that crime rates would be at minimum if there was no consequences at all.
With no penalties, somebody could simply kill or rape your mother, sister or child and move in next door and live a nice and happy life in front of your very eyes, without society doing anything about it! Bare in mind now that this is the situation where the probability of your mother, sister or child being abused, robbed or killed is minimized!
Would it be reasonable to go trough with this demobilization that would spare lots of innocent people all the pain of getting robbed and abused, given that those criminals still out there can do anything they want and go free?