(This is just a post from my personal perspective, but I hope it’s helpful.)
Every few weeks or so, someone contacts me and says “Hey Matt, there’s page out on the web about me that I really don’t like. Is there any way to remove it from Google’s index?” People don’t usually say it like that. More likely, they say “There’s this person making crazy claims about me on the web, and the stuff they say is just off-the-wall. Can Google remove this crazy person’s page?” Or “Everybody knows that this crazy person is posting lies and twisting people’s words. Is there anything you can do about it?”
I’ve responded to this so many times that I thought I’d write up a complete response. Now when people ask me some form of this question, I can just point them to this blog post. So here’s the sort of reply that I would normally send back:
Unfortunately there’s not much I can do. The page you pointed out is not spam, and pretty much the only removals (at least in the U.S., which is what I know about) that we do for legal reasons are if a court orders us. We typically say that if person A doesn’t like a webpage B, only removing page B out of Google’s search results doesn’t do any good because webpage B is still there (e.g. it can be found by going to it directly or through other search engines). In that sense, the presence of that page in Google’s index is just reflecting the fact that the page exists on the wider web.
The best actions for you from our perspective can be one of a couple options. Either contact whoever put up webpage B and convince them to modify or to take the page down. Or if the page is doing something against the law, get a court to agree with you and force webpage B to be removed or changed. We really don’t want to be taking sides in a he-said/she-said dispute, so that’s why we typically say “Get the page fixed, changed, or removed on the web and then Google will update our index with those changes the next time that we crawl that page.” Our policies outside the U.S. might be different; I’m not as familiar with how legal stuff works outside the U.S.
There you have it. People usually aren’t happy to hear that reply, but I hope they can understand the reasoning behind it. If you were creating your own search engine, I also hope that you’d come to pretty much the same conclusion. The official documentation page on how to remove a page from Google’s search results says essentially the same thing, but I wanted to give a little more context.