What do my cats tail movements mean?

I just read that a flicking tail means agitation. I don't believe that. Both my cats flick their tails when they are purring. I think cat tail signals are many and complex. Do you have any idea about your cats tail signals.
Answers:
My cat does that on a regular basis and he either purrs or plays with my hand. I don't think it's a sign of agitation and I have to agree with you on that one. Cats are very complicated creatures to decipher.
The tip of the tail flicks and shakes when they are happy.

It is a different sort of flicking when the cat is angry.
well, I know when I am petting a cat and the tail gets going, pretty soon they will be overstimulated and bite or swat at me!

that's my experience. I guess you have super nice cats.
like moving the ANTENNAS..confused.catch from the air
a flicking tail can mean agitation or excitement. If their ears are flat and their tails are flicking then they are agitated
when they twitch their upright tails forward ,that's a sign of agitation.Normal tail flicking (side to side)is.well,.normal.
I think animals have different moods/dispositions just like humans. What makes one mad can make another not care.
when it really wags he is cross
There are distinct signals from your cats; when coming towards you, if the tail is straight with the end curved over like a walking stick, this is a greeting and the cat is pleased to see you. Lashing the tail from side to side can mean both anger and fear. The tail becoming bushy means sheer terror and is a request for immediate rescue. Twitching the tail has several meanings; where is can mean agitation, it can also denote playfulness or be a signal that whatever you are doing, the cat has had enough!
purring isn't always an indication that the cat is happy either. i've had one purr its head off and be pissed at the same time.
When a cats tail is thrashing fast it means they are annoyed. If it is slow and it appears they are waving their tail about it means they are happy. If a cats tail is not moving at all really, it means they are either in a neutral mood or are very relaxed (nearly asleep).
When your cat is walking along, minding its own business, tail down...call it by name and its tail will shoot straight up in the air..it's a greeting cats use to say 'Hello, I know and trust you." If your cat DOESN'T do this - then you should learn why...
I have a fixed male Russian Blue. When he wags his tail, it means that he is agitated. Keep on petting him and he will get you with his razor sharp claws. I have to take him to the vet to get his nails clipped.

If the tail is in a position like a ? (question mark), they could be in heat--especially a female.
well it depends. if the cat is lightly flicking it and her eyes are closed.she's happy

but a wide flick that is up and down that is not a good sign. my cat does that when we pick her up becasue she gets nervous and her eyes get all big and she makes herself really heavy and tense. so..ya. that's not good.

and when the tail is slowly moving around in the air she's just neutral and in a good mood.

its true though you do learn the special movements for your cat. i don't even think about it anymore i just know when to leave her alone and how much i can tease her before she'll start swiping me.
bottom of the tail= mad or can mean they are happy
tail is in the air= happy to see you
hole tail is moving= happy
sharp whiping of their tails means that they are pissed.
It can mean they are happy