If you don't want it on the internet, don't post it. Assuming anything can ever be made to disappear from the internet is naive, and if people become aware you are, it'll just get Streisanded and become even more widely posted.
There are two sides to this argument. I argue both. All the fucking time.
If you're in the business of providing public content that's well-known, to the public, then allowing it to be archived makes a lot of sense.
If you're providing user-generated content I'd argue that the case for allowing archival is extended even more so. Sites that violate this, and Quora comes specifically to mind, are violating what many, myself included, consider to be part of the social contract of the Web.
On the other hand, if you're an individual, and you are posting your own content and ramblings, and circumstances change for whatever reason: you've got a job, you've lost a job, you're married, you're divorced, you're getting divorced, your child is at war in a foreign country, a foreign country is at war with yours, or you're just sick of the crap you wrote when you were young and arrogant and now and old and arrogant you wants it gone: I'm pretty willing to grant you that right.
If you've committed some terrible crime against humanity, or just a human, and have been fairly tried and convicted of it, I'd probably not give you the right to remove large bits of that information.
And yes, there are vast fields, deserts, tundras, plains, steppes, ice-fields, and oceans of grey about all of this.
Barbra Streisand got Streisanded because she is Streisand.
Ahmed's Falafel Hut likely wouldn't suffer the same fate. His Q-score is somewhat lower, and there's only so much real estate in the public consciousness.
Things disappear from the internet, for good, all the time.
Also, if people become aware someone is naive they automatically are dicks to them? Regardless of wether that information is actually of interest to anyone, just because someone wants to take something down, they should not ever be able to?
Some people act and think like that that, yeah. But to accept this as the baseline of human behaviour is, well, not for me. This entitledness to watch the lives of others from the the dark may have been bred by reality TV or whatever; but it's more a personality flaw and an addiction, a useless misfiring of synapses become culture, than a cornerstone of an information age.
