OK, here is the reason why censorship in any form should be opposed. It's nothing to do with bleeding-heart liberalism or sympathising with criminals, or these sorts of arguments the pro-censorship lobby use in arguing the issue. The issue is more fundamental than that.
Suppose we have four premises, A, B, C and D. A is something really offensive and unnecessary in the eyes of the general community, like child porn or bomb-making instructions. B is maybe political dissent, C is discussion of security issues, and D is simply what positions people like doing "it" in.
Now, if we all agree that A should be banned, we set up and enable the censorship infrastructure that makes this possible, well and good. But then comes the problem of the old "inch and mile" principle. Having successfully censored A, we've now created the ability to censor anything else. The door is now open for wowsers and do-gooders (and that doesn't mean you are one of them) to start agitating to ban B, C, and D. And they WILL. Some people are never satisfied, once they've banned one thing they'll start in on something else. Once that door is opened, it will never stop. The right political maneuvering will be able to allow ANYTHING to be banned by careful use of FUD and propaganda, and freedom as we know it dies.
So we're caught between Scylla and Charybdis. On the one hand, the only way to guarantee our freedom from those who would ban anything they don't like is to allow everything, even the things we don't like. On the other hand, allowing total freedom allows society's worst elements to roam at large and prey on the innocent. The question then becomes one of balancing freedom against safety; by refusing to censor A, and then studying those we catch committing A, we can look at why and how they got that way and work out ways to circumvent the societal problems that caused them to do so. Treat the disease, not the symptom, so to speak. Again, that's not about sympathising with criminals, it's about preventing the circumstances that create them in the first place. If you just suppress the symptom, all you get is an arms race where people endlessly try to circumvent censorship and endlessly try to lock it down again, and the original problem never gets solved.
I also have nieces, and if a sexual predator messed with them, believe me I'd be the first in line to work the bastard over with a carton-knife and a soldering-iron. But I cannot in clear conscience demand censorship, even in the name of protecting my nieces. Too much will be taken away from them if we allow censorship, and where is the value of life if we must all live in fear of offending some hyper-sensitive self-righteous git? So what I've done is to educate them, to make them aware of the dangers, how to spot them, and to take precautions to ensure their safety. It's all I can do.
Because I want my nieces to grow up into a world where they can express their ideas and opinions freely, to reach their full potential, not to cower in fear wondering if they're going to get silenced or in trouble for every little thing they say or do.