Stack Exchange is supposed to be a fusion of forum elements and wiki elements, among other things. Although we are not Wikipedia and don't try to enforce all of the same rules or principles that they do, there is one particular principle that is very important to us: Verifiability.
Loosely speaking, verifiable claims fall into a few distinct categories:
Claims that are directly observable or testable. "The sky is blue." "if you overcook a piece of meat, it will dry out."
Claims published in reliable third-party sources: Peer-reviewed journals, books from reputable culinary professionals, etc. See my suggested hierarchy of sources.
Self-referencing claims, e.g. I am happy right now, as long as there is no reasonable reason to suspect that the author is lying or exaggerating.
It's actually wrong to say that we expect or require citations on every post. You may sometimes see people say "" as a tongue-in-cheek reference to the Wikipedia template, or maybe you'll see a community member or moderator say "please cite reliable sources" if a particular question is expected to generate a lot of noise. Either way, these people are talking about questionable claims. An incomplete list of examples would be:
- Popular myths. "Adding oil to pasta water prevents sticking."
- Popular half-truths. "You should always add cold oil to a hot pan."
- Popular beliefs that are plausible but simply unproven or oversimplified. Cooking destroys nutrients in food. (sure, but it also increases bioavailability of the ones that remain)
- Claims which simply seem to have been pulled from thin air. I've heard that sugar loses flavor over time. Huh? Where did you hear that? You'll more often find these types of claims in questions than answers.
Often you'll find people defending questionable claims as "common knowledge" or "common sense". Sometimes, they'll be based on real facts but jump to bizarre conclusions based on logical fallacies. That is what we don't want to see here.
One reason why we don't allow most nutrition questions is that the vast majority of "information" being dispensed about it clearly falls under the "questionable" heading. But it's prevalent in cooking too, with cooks apparently being especially prone to superstition inherited from centuries past.
I still hear people saying that searing meat "locks in" juices, or that you need to soak beans before cooking them. Those claims are demonstrably wrong and I can just point them to Hervé This, but there are many other claims which have yet to be put under the microscope and I don't necessarily have time to do the experiments myself. So,  it is.
Citations are especially important when discussing subjects that can't be directly observed or tested in a home setting. Of particular note are the subjects of food safety and culinary-related nutrition. Unless you're an experienced microbiologist, you're not qualified to be making first-hand statements about bacterial growth. Leave that to the experts.
So to recap all of this: We don't expect every claim to have a citation, but we do expect them to be verifiable. Generally speaking, if you're answering a how question, the burden of proof is fairly low; either it works or it doesn't, and people will vote accordingly. But if you're answering other types of questions (especially "why" questions) then please think very carefully about whether or not the information you're providing is reliable.
As Yossarian says, you're welcome to post whatever you want as an answer, but you will be voted down and/or criticized if you don't make a reasonable effort. It is completely acceptable for people to do this and generally not acceptable to reply with a snarky remark about the burden of proof. Not that I'm accusing anyone specifically, just putting it out there as a general tip.
If you can't prove it or at least back it up, don't post it here. Please.