It's a common trope that people fear public speaking more than they fear death.
This list of common fears actually puts it at number four. This one has it number two. The Huffington Post has it at number one. Wikipedia has it in a list that isn't ranked, but it's the only item that's given a full paragraph.
So fear of speaking in public may vary from list to list, but it's up there. Alongside genuine physical dangers of all kinds.
Susan Cain's book Quiet: The Power of Introverts in a World That Can't Stop Talking (awesome book, by the way) provides a very interesting possibility. She cites a theory by sociobiologist E.O. Wilson, which credits this fear to the many millennia we spent living on the African savannah. Back then, we were, at all times, potential prey. Being watched intently meant we were being stalked by something that would pounce on us and eat us.
Scientist Rupert Sheldrake has theorized that we developed the sensation of knowing when we're being watched in order to survive this exact feature of our evolution. He goes into it elaborately here, connecting it with the phenomenon of pets knowing when their owners are coming home.
So what's the natural reaction to being hunted by a large wild animal? Standing your ground and speaking clearly, with a relaxed demeanour? Speaking as if you're just chatting with a friend, cracking jokes?
As Cain puts it: "Hundreds of thousands of years of evolution urge us to get the hell off the stage, where we can mistake the gaze of spectators for the glint in a predator's eye."
She adds that this is "why exhortations to imagine the audience in the nude don't help nervous speakers; naked lions are just as dangerous as elegantly dressed ones."
This theory ties in neatly with a bit of animal behaviour explained in Steven Budiansky's book The Character of Cats.
Cats express fear through the widening of their pupils, as well as offensive aggression. A cat about to pounce, or who's ready to fight "will narrow his eyes in a beady-eyed stare" as Budiansky describes it. A cat who blinks and turns away signals submission.
So direct eye contact is interpreted as a threat - either from a rival, or from the interest of a predator.
Budiansky says "This, incidentally, may explain the perverse but pretty nearly undeniable fact that cats always seem to plop down with unerring instinct in the lap of the one guest who hates cats." The cat lovers stare at the cat, as well as try to engage her. The cat haters, those indifferent to cats, or those allergic to cats, look at them less, if at all. The cat interprets their genuine lack of interest as non-threatening, and voila, that's where I'm going to sit.
Perhaps public speaking would be less anxiety provoking if no one was watching. Maybe that's why people vlog so fearlessly and frequently.