Fred agrees that the incarceration of violent mentally ill is needed to protect people from violence. Fred agrees that he benefits as much as anyone else does from that protection. The specific point he disagrees with is whether or not he should have to pay for that protection.
If you don't mind, go read "The Law" by Frederic Bastiat. The text is available online and it's only about 50 pages. Let me know what you think.
Why bother? The issue is that you want to consume public services but you don't want to pay for them. Reading books by obscure 19th century guys won't really do in lieu of payment.