There are two things here that I wish were not socially accepted: the demonization of even small amounts of body fat, and banning content you dislike "for their own good".
Now, those pro-anorexia blogs are creepy and disheartening; I looked through some a while back, and they really are as sad as they sound. If Tumblr's goal is to prevent more teenagers from latching onto that subculture, there are a few things they might try. They could stick warning banners up on the blogs in question, visibly registering their protest without going so far as to remove content. Or they might shrug regretfully and say there's not much they can do, since they hardly have a monopoly on the blogging platform market, which would be true. Setting themselves up as censors was not their only option, and as far as I'm concerned, it should have been pretty far down on the list of ideas.
In general, I'm uncomfortable with the impulse to try to stop people from saying messages that you don't want others to hear.
As rational individuals, we can decide where to draw the line. This vastly increases the surface area of critical attacks - the line will seem arbitrary, and there will always be boundary cases which could go one way or the other. "Why this and not that?" will be heard often. It's an easy target. So yes, the easy answer is that all discourse should be allowed.
But really, I don't want people advocating that bullshit to teenagers.
1. Freedom of speech is important, but this is a special case.
2. This stuff really is harmful. I don't want bad people exposing children to sex/communism/homosexuality/anorexia/witchcraft/whatever.
3. We're only going to censor $TOPIC_OF_THE_DAY. This is not a slippery slope.
4. Be reasonable.
Of course in this case, the stakes aren't that high, since it's easy for censored blogs to move away from Tumblr. This policy is more about social signaling than about seriously trying to help anyone.
I agree with you, it's awfully two faced of the popular organizations. Historically, if you really wanted freedom of speech, you pretty much had to own the printing press. I think the same thing is largely true now. You gotta own the server that hosts the blog. no one out there will protect you.
Tumbler may choose to censor other stuff, they will not choose to censor other stuff simply because they chose to censor this. They will censor other stuff because the other stuff is offensive (or not, they still have choices to make).
Also, i saw the phrase slippery slope and dismissed that part of the argument. It's meme-ridden fuzzy thinking at best. the "for the greater good" is imho suspect because of the Orwellian emotional ties to big brother.
So, i'll say both clauses of your or are true.
Well obviously. That's not the form of the argument here, though. The argument is that, once Tumblr gets used to censoring one view they consider harmful, they're more likely to censor others. The claim being made is not one of logical implication, but of conditional probability.
Livecasting of own suicide: freedom of expression + freedom to make choices with regard to own life.
Edit: This is not to imply that Tumblr is not entitled to do whatever they damn please with their own website. But, should someone build a website specifically for livecasting suicides I would very much disagree with its censorship.
Put a warning on it saying that it's NSFL, maybe run a free banner ad next to it for a suicide prevention hotline. Those things are reasonable, productive responses. Censorship of the video would be as symbolic as waving a flag, and about as useful.
Censoring the video may actually have prevented the suicide, because viewers were egging him on. It's hard to know.