My last several years as a police detective was spent investigating child abuse and sexual assault crimes. Many of those kinds of crimes often lead to murder of the victim. During my investigations I often had to counsel the parents, usually the father, to not harm the suspect. If the father harms or kills the suspect, then the father must go to jail. Then the child must get through a very rough time in his / her life without their father. Parents, both parents, must be there to support and help their child heal. Because our system is set up on the rule of law, we must let that system work. Does it always? No, certainly not. Do sex offenders always get the punishment they deserve? No, they don't. Why?
Too often when parents try to take matters into their own hands, they harm the criminal case. An investigator's best weapon against perverts is the ability to conduct a forensic interview. Often that interview is successful because the investigator is able to take him by surprise and trip him up on his own statements. When a parent or other adult confronts an abuser, the suspect is forewarned and more difficult to get a confession from. Sometimes they will flee the jurisdiction before the police can get their hands on them. I've never known a child abuser who has only done it one time. If the case is jeopardized by well meaning amateurs, not only is that case harmed, so are all of the other crimes he (mostly men) has committed. I never stopped with just one case, but once I got a confession in my cases, I always went fishing for others in his past.
Most sex crimes lack an important element; that of a third party witness to the crime. Even with physical evidence, a confession is very important to obtaining a conviction. Criminal defendants and their attorneys will invent very creative ways to explain how the suspect's DNA came to be on or in the victim. The trick is, to convince the jury that the defendant is guilty. There is almost never a guilty plea in such crimes, at least at first. Once the defense attorney sees a solid case against their client, they usually convince them to plead guilty and try for a reduced sentence. I've been successful in nearly all of my cases presented to the DA, with many guilty pleas and convictions. I've sent many sexual offenders to prison, and the stories about child abusers in prison is NOT a myth.
It is a very macho thing to sit back and say what you would do, but until it happens, you really don't know. Harm the suspect and there's a good chance he will get away with a light prison sentence, while you sit in prison as "an example" to not take the law into your own hands.
Before you dismiss what I have to say because I've never been there, both of my children (now adults) were sexually abused as children. I've been there. Twice.