Evidently (according to many sources including the web-page quoted here), "a person suffering from this condition feels that somewhere in the world, a duck or a goose is watching him/her (not attacking or touching, simply watching the individual)."
This page explains with apparent empathy that "There are many kinds of seemingly irrational fears and phobias prevalent in the world. What might be laughing matter to people, is not so to a phobic."
As you can see, dear reader, the photograph atop this posting is of a female and male Mallard. I took it when I was in Central Park a few weeks ago. Anyone coming upon this pair of ducks would notice that the male is preening, but if the person who happened to come upon these ducks was suffering from Anatidaephobia, he/she might have cause for alarm; for it does seem as if the male is watching as he preens.
Btw, the aforementioned page explains that the word "Anatidaephobia is derived from a Greek word ‘Anatidae’ which means ducks, geese or other water fowls, and phobos is Greek for dread/fear."
They also claim that "... Anatidaephobia or the fear of ducks might have sprung due to a negative or traumatic incident related to ducks or geese. Such birds are known to have violent tendencies and are often known to attack people without any provocation. Often, they swoop down to steal food or simply take a nip... A child might have directly or indirectly experienced such an episode. She/he might have experienced the flapping sound made by the bird’s large wings..." (such as the action this Mallard is "performing" in the picture directly below, which I took when I encountered him in the park.
This web-page reminds its readers that "It is important that family and friends support the individual instead of teasing/laughing at them or doing other things to entice their Anatidaephobia."
The following images of a few ducks whom I have seen in NYC can help one understand how a person suffering from Anatidaephobia might think a duck is staring at them, such as these female and male Wood ducks swimming in The Pond thats within Central Park and seen in the following pics (respectively)...
..... or as evidenced in the images of male Northern Shovelers (swimming in Central Park's lake) that are below.
A Khaki Campbell duck can also look as if he/she is glaring at someone as you might surmise from the next image which I took when I saw this bird type on a bank of the Hudson River.
Another duck who spends time at the Hudson River is a Muscovy. She certainly gives the illusion that she is staring down whatever she is looking at as evidenced in the the nest set of photos.
The Canadian geese seen directly below (in photos I took of them in Central Park) illustrate the point of "the stare" as well as wing flapping that might give cause for concern to Anatidaephobia sufferers.
Canadian geese are featured in volume two of the Words In Our Beak book series.
Book Seller Info: http://bit.ly/2AFZDCz
Barnes & Noble On-Line: http://bit.ly/2AAnB26
book culture On Columbus (a bookstore on the UWS in NYC): http://bit.ly/2FsC1Uf
Volume Two (pictured within this post): ISBN: 9780996378536
Book Seller Info: http://bit.ly/2q75g8e
Barnes & Noble On-Line: http://bit.ly/2G65m6H
Volume Three (pictured within this post): ISBN: 978099637853
Now available on Amazon @ https://amzn.to/2IYkmpA and can be ordered from any place selling books by giving them the title and/or ISBN, which once again is 978099637853.