From the time to time I play Minecraft multiplayer, I spot a certain kind of server in my search of a good one to play one. In the server tags, they put "griefing". Usually it means they allow it. One reason I can think of why they'd put that tag in is to let people know that they do in fact allow griefing. But why??? Why would any server owner in their right mind allow griefing? To me, it seems like they're trying to attract EVERYONE to their server, including the lowest common denominator.

I dunno, maybe there's a super simple answer that I can't figure out due to my currently sugar-addled brain. Oh well. Thankfully these sort of servers aren't the majority.

Because competition.
Why build the best city when your opposition can't ever build a good one?
Think about it.

Because its part of the vanilla mc experience. Nothing is permanent, there's no mechanic to ensure protection against it, and its part of the idea of being an open world where you can do anything. Some people choose to hide, some start groups and raid, etc. It always seemed like the intention of mc is to give a minimal system to see all the things people can do. Its cutting out a whole realm of possibility to not allow it.

With that said I hate griefing passionately so I pick nongriefing servers.

It could also be because enforcing non-griefing is a pain in the ass. Every, and I mean every, anti-griefing plugin has holes in it that the more cunning griefers take advantage of. Then you have to go to the trouble of finding whodunit using your block logging plugin(and hope your MySQL server wasn't down at the time. ). Lets not forget that many griefers have alts and proxies as well.
But I agree with Doivid. Griefing is terrible and wrecks the experience for anybody who just wants to build.

It could be fitting for some servers, and others probably don't have the time. I personally feel like griefing isn't as bad as people make it out to be. (Plus, if someone dislikes this rule on some servers, either don't join or don't complain when it happens.)