This is a terribly difficult question to answer for several reasons. First, the "origin" of myths is deep in prehistory since every literate society stepped onto the historical stage with mythology in full blossom. It is likely that one should not even think of it as a question of origin, since storytelling seems intrinsic to humanity, and one can imagine stories interweaving, becoming traditional while being in constant flux until they became something that we might call "myth." The problem about finding the origin of all this finds analogy in the question of the origin of humanity itself. When did the first man and woman step onto the stage? How would we even define those individuals. It was a blurred, gradual process that we now understand was made even more complex by the interaction with other subspecies of humans. So, too, myth likely had blurred origins with creation, change, blending, etc., occurring over hundreds of generations.

Then there is the question of the term "myth" and what that means - a second problem when it comes to answering your question. In my Introduction to the Folklore, I address some of the issues associated with this word:

People use this term [i.e. myth] awkwardly. In a European context, myths tend to be the artificial constructs of ancient and Classical-era priests or literate people who sought to weave folk traditions into a comprehensive whole. The exercise often had political purposes, designed to provide diverse people with a single set of beliefs and stories. By reconciling similar traditions, the shared culture of these groups could be seen as more important than the differences, justifying the central rule of the king and his priests. Myth is also a way of organizing and reconciling folk traditions, which by their nature can be contradictory and highly localized. Myth tends, however, to make gods of supernatural beings, giving those powerful entities a status – for modern readers – similar to the Judeo-Christian-Islamic God, even when this comparison is not justified. Of course, it is also important to point out that myths were stories that were told – and then written down – and they were different from religion itself. Many myths were simply the shared cultural inheritance of a group of people.

In general, the word myth is best set aside when discussing more recent folk traditions, recognizing its proper status as a literary genre. Nonetheless, ancient documents recording myths can assist in understanding the history of various stories and beliefs. The authors of these texts were, after all, the first folklorists, and they were the only ones coming close to practicing the craft at the time.

Some folklorists carelessly use the term myth to denote those legends that deal with a fantastic, remote time. This primal era saw the creation of many familiar things such as day and night, fire, animals, people, mountains, and all other aspects of the present world. Folklorists properly refer to these stories as etiological legends explaining the origin of things. Sometimes, however, people interchange etiological legends with the word myth. The problem with this is that “myth” can imply something that is inherently wrong, linked to “primitive” superstitious beliefs. When the term “myth” is used for the folklore of existing cultures or for the traditions that were viable only a generation or more ago, it can take on an insulting, derogatory tone. It is best to reserve the word “myth” for ancient and Classical-era texts.

The core problem here as it relates to your question is the idea that we are talking exclusively about some sort of religious texts. Likely, pre-literate people did not think in those terms. They told stories about a variety of things, some to be believed and some for pure entertainment. Of those that were told to be believed, some were about culture heroes and others were about fantastic supernatural entities, some of which were feared, and some of which became woven with more hopeful adoration.

How did these stories originate? People might speculate about eating drug-laden plants or other things, but we don't know if that's the case, and we have no reason to imagine that sort of thing.

The thing that is clear is that many of the mythologies are related: a group of Indo-European stories diffused during prehistory with the language (sometimes carried my migrants, and sometimes just travelling on their own). Other ancient stories seem less likely to be related, and this points to several points of origin. This means that these stories were welling up somehow in several places and then diffusing through time and place.

With the rise of Urban Legends, several folklorists attempted to track down the origin of several of these stories. This presented an opportunity to answer your question in modern terms, since these Urban Legends seemed to appear spontaneously and then to disappear. Again, an excerpt from my Introduction to Folklore:

The answer to this question [that is, the question about origins] is somewhere between "we don't know" and "it's just what people do" – that is, they invent these sorts of stories. Several folklorists, including the late Alan Dundes and Jan Harold Brunvand, recognized an opportunity with recent urban legends to finally track down "the source," the point of creation, to better understand how stories originate. For the most part, they were unable to find the point/person of origin to any general degree of satisfaction. It is a maddening question, and much like the proverbial chicken and the egg, it isn't likely to be resolved.

People tell stories. People repeat stories. And as they repeat them, people modify stories, which sometimes results in the birth of new stories. There might have been some highly imaginative, creative people who invented stories at some point, but that sort of person has yet to be identified in the annals of folklore studies. Folklorists often asked renowned storytellers to tell a new story, to invent something that they had not heard. Without exception, these requests were refused by the storytellers who explained that while they repeated stories, they did not invent them. In general, it may be best to consider the possibility that the process of repetition and transmission is the source of much of the creativity that is evidenced in the international library of oral tradition.

One example may help shed light on the creative process: the Cornish droll tellers were known for their wild adaptation of the material they heard. Their counterparts in Ireland were the seanchaithe, professional storytellers who prided themselves in the faithful recitation of stories they had heard, as close to the original as possible. Perhaps in this, we can see the opportunity for new stories to be born, and indeed, Cornish oral tradition includes more than its fair share of distinct subtypes (i.e. variants) of legends and folktales, perhaps offering a hint as to how these things may come into existence.