Without going into the psychology of the thing too deeply, lets just say that it is in our blood. We humans have a long association with agrarian ways including livestock husbandry. This goes back to before recorded history. Chickens started out first and foremost as livestock, providing food and some few other benefits to early man. They were also used to provide sporting diversion from life's more humdrum ways. In fact, evidence supports that this was the reason the difficult task of domestication was first attempted (this is fact: DO NOT get started on the morality of cockfighting, please!).
Just take a look at our language for a few clues:
Does anyone count their chickens before they hatch?
If you don't wanna fight, you are called a what - a chicken!
Business men are admonished to NOT put their eggs in one basket.
WHen a man is full of himself, he's the "Cock 'o the Walk"... and so on.
Chickens have been a part of our existence for a long time, New Age "Hug-A-Tree" Warm and Fuzziness notwithstanding. Sure, they provide eggs and meat. And yes, they are relaxing, calming and personality-laden. They give us something purposeful to occupy ourselves with, too. Some even consider them as crucial elements of the latest goofy craze: 'Provincial Feng Shui' practice. All well and good, I suppose.
But one of the main reasons we love the silly things, if not THE MAIN REASON, is simply that humans and chickens belong together... we're old friends.