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From what I understand it's mostly just a myth. As for any sort of shifting I know therians can experience something called...p-shifting? I think that's what they call it. When their mind state shifts more towards their animal form. Not sure if it has to do with the moon or not, but I'm sure it can have an effect on certain individuals.

Lycans, lycanthropes, werewolves, whatever you want to call them, do not and have never existed on this planet. There are those otherkin that use the term to describe themselves but they seem to be more inclined to describe themselves as anthropomorphic wolf-men than shapeshifters.
There are also otherkin who refer to themselves as shapeshifters, but they do not rely on an outside source (such a the moon) as a trigger.

The human/earth werewolf myth goes back a while and the word lycanthropy comes from greek. Here's the Wikipedia article.
All myths originate from something, yes, but that "something" can be as simple as a fear of the dark, or a person who's got a horrible temper and mood swings or the glimpse of a passing animal in the night. There are millions of mental differences between people, some are outright disorders. Dissociative identity disorder (or multiple identity disorder) can have been the source of stories and myths such as the famous Jekyll and Hyde, which does not prove that they existed, or that they were in any way superhuman. Human beings like to be special, they like the world to be special, that alone is enough to create massive, fantastic, worlds and stories. We have libraries full of the proof to that.

P-shifting is actually short for "physical shifting" which is an impossibility, though many people will try to convince you otherwise. The problem is one of the nature of mass. It simply cannot shift around without causing serious problems, plus it cannot change quantities as would be required to turn into say a wolf 100 pound wolf when you're a 180 pound human.

There's also mental shifting, astral shifting, dream shifting, partial shifting, and the idea of contherianism which means that you're constantly in a state of mental shift - i.e. you see the world through an animals eyes always.

ahhh I meant mental-shifting then. Couldn't remember the term.

I'm a therian myself, so I have had first-hand experience with shifting. There are many types of shifts, which have been listed above. By far the most controversial (and the most nonexistent in my opinion, though I suppose you never know...) would be physical shifting, in which a physical body shifts into another physical form. The closest shift to the physical that is experienced is phantom shifting, a wonderful or awful experience depending on the therian. In Phantom shifts the therian experiences a "phantom limb" sort of phenomenon, in which they feel as if they have extra limbs that are typical of their species, such as wings, tails, etc. They of course do not exist on the Earthly plane, but it feels to the therian that they actually have these limbs. This is quite similar to the phantom limb phenomenon experienced by amputees, which I won't go into depth about here. Phantom shifts as I said can be good or bad, they can either bring joy at feeling that you have the body you were meant for (I definitely feel joyful about it, because I'm one of the few that suffers from species-dysphoria, so having my body regained temporarily is amazing) or it can invoke feelings of sadness or loss and serve as a reminder of the body one was supposed to have.

The most common shift is the mental shift, which I have also experienced, in which the therian sort of shifts into a different gear and begins thinking like their animal or mentally becoming their animal. Mentally, they are the animal.

None of these shifts are affected by the moon or any outside force, though I think they can be brought on by stress, anxiety, etc. or deep meditation.

This is just an overview of some more common and interesting forms of shifting, though there are many others. If you have any more questions, there are plenty of online sites that can help, or feel free to note me. Hope this helped you!

It could be. I personally believe reincarnation is behind therians, and phantom limbs are only a manifestation of their true form.

i am a were or cat kin weres can physically shift but must work for it moon phases can affect us but not make us shift a good one is morphosephram by sum william guy redface