The short answer is that nobody seems to know. Yet.

What seems likely is that picky eating is not a unitary phenomenon - for some people it's to do with their ability to swallow, others have a strong sensitivity to taste and texture (find out if you're a "Super-Taster"), or an over-active gagging reflex. Some may have had a traumatic early experience with food of some kind, prior to which their eating was "normal". For others it may have started as an issue of autonomy.

Most picky eaters can only guess what caused their pickiness. Personally, I wonder whether picky eating might not persist through adulthood because a critical developmental window is missed (for some reason). Many abilities that develop in early childhood develop only at a certain stage - vision is one, language is another - perhaps if the opportunity for learning to accept new foods is missed, that is what makes it difficult to learn it later. If so, adults then may learn to be less picky, food by food, but it would explain why it often requires hard work, good luck, and perseverence.

Another possibility is that picky eating has a neurological (and/or genetic) cause. I gather it has been associated with OCD (Obsessive Compulsive Disorder) and with autistic spectrum disorders.

Here's what they told me at Anred, a website for Anorexia & Related Eating Disorders, when I asked them:

"The causes of picky eating are several. Some adults were super-tasters
as children, and they remain so as adults. Sometimes picky eating is a
manifestation of obsessive/compulsive disorder. Sometimes it signifies
a power struggle -- with a living person or even continuation of a
pattern that was created long ago with someone who is now gone or
deceased. Sometimes picky eating is a sign of a cautious person who has
found his or her comfort zone and does not care to adventure out of it
with new and different foods. And sometimes picky eating is a symbol of
independence: It's my body and my life, and I'll do as I please
regardless of what anyone else thinks! I'll even pay the price of
social embarrassment to make my point."

I'm not sure I quite agree with that last point, but then as a picky eater, I would say that, wouldn't I?

It seems to me that there are different types of picky eating, as well as differing degrees, and there's no good reason that I can see to suppose that they all have a single cause, or even a common cause, given the diversity in people's experiences.

If you have a theory, we'd love to hear it.