I was reading on some forum where someone, perhaps an admin, that it's a privately owned domain, i.e. website, and we, the staff, have right to censor whatever we dislike. The person went on to make an interesting anaogy that you have no right to insult me or say things where I don't like in my home. Is it really true? Most of the forums are privately owned by someone and so are the blogs. I would agree that no one has any right to make hate speech, inflamatory remarks, racial slurs, etc. But suppose the owner is a theist, then does it mean an atheists coming to the forums have no right to express his views or negate the views of theists? What is your take on this? Please let me know it. Thanks.
If you own a website, you can do whatever you want in your webspace, as long as you do nothing illegal according to the laws in your country.
That means that you can have a blog and approve only the comments that you like, and delete all the others. It also means that in a forum, the owners can decide which posts should not be approved, which ones should be deleted, who should be banned, who should become a moderator, and so on.
Is this fair? I guess it is. Your website, your rules, right? Of course this is likely to make your website biased, but that's how most websites are anyway.

The internet is the best place as far as freedom of speech is concerned (well, at least in some countries). Why? Because although you can't always say what you want on other people's websites, you can always get your own website. Nowadays you can easily get a blog for free, so freedom of speech is not even a matter of money.
Great explanation Kooyeen, I totally agree!