Do you think when you say ‘Hi’ to your cats and they give the barest flick of their tail, they’re saying ‘Hi’ back…or it’s the cat equivalent of rolling their eyes?
They’re saying: “I have no idea what you’re saying to me, I’m a cat.”
The barest flick means “I haven’t forgiven you for not being here to cater to me all day.”
This. 
“Did I give you permission to address me, underling?”
If you do a gentle “trill”, with a rising pitch, like a question, “Mrrrow?” and look away, while wiggling your fingers a little, most cats, even strangers, will come to you in a friendly way. The sound imitates a mother cat calling the kittens to suckle, and they never forget it.
You can test it. Give them a slow blink ( Google that to see what it looks like) If you get a slow blink back, that is a friendly gesture. Tailflicking, IMHO doesnt mean much, communicationwise. Rather it means a small inner shift from one state (eg resting) to another , like thinking about getting up.
Maybe it means, “I thought about acknowledging you. I’ll let you know what I come up.”
edit: Given they often look away when giving the merest tail flick, maybe it means “Sup.”
Finally! The thread I’ve been waiting for all my life!
You’re all right.
I think they’re trying to say “Stop anthropomorphizing me.”
Whenever I see a cat go by, I give him a psst-psst. He’ll quickly turn his head to glare at me and i go - Hah! Made you look. Pisses them off every time.
Psssst sounds like a cat hissing, ( equivalent of yelling: hey bitch!) so the glaring looks probably are startled looks.
This website is, IMHO, the best resource for learning cat language.
http://messybeast.com/cat_talk2.htm
The interrogative trill is used by female cats in heat to indicate a highly romantic state of being. If you make that noise and find a Tom biting the back of your neck watch out!
Thanks! That’s like a frickin’ thesis! Bookmarked for later. 
Generally, one should speak to a cat only in Hebrew.
As I understand it both cats and dogs assert dominance by sniffing the butt of the other. True or not that is definitely not anthropomorphic behavior.
Am I the only cat person here who meows at my cats, and they meow right back?
Nope. I do it.