evolution - Why do squirrels have twitchy bushy tails?

Whenever I see a squirrel in the woods, it is always the big bushy tail flipping around that gets my attention first. A pray animal with a big bushy flag calling attention to it's self seems to be counter survival, a big flag waving here I am, come eat me.

*Image from Wikisource

Video link, of tail twitching

Why do squirrels have twitchy bushy tails?

Edit to Clarify Squirrels do not have a high reproduction rate, there are multiple difference between species but most seem to average about half a dozen young per year.. While a pair of rabbits can (though unlikely) create 1300 offspring in a year Wild rabbit and squirrels have similar coloring and predators. There are of course multiple differences between rabbits and squirrels. Given the difference in reproduction and a big wavy flag that says come eat me. It seems that if there is a rabbit and a squirrel sitting on the forest floor eating breakfast, the one waving the flag is most likely to be seen and eaten.

Answer

The obvious answer is that having a balancing ballast is incredibly handy for some of the death defying jumps squirrels perform. The tail is needed for that.

You make the assumption that an inconspicuous tail would be bad for predation. I would challenge that assumption, but I am making an educated guess so feel free to debate this.

Tail flagging in ground squirrels is used to deter predators and communicate vigilance. Perhaps something similar occurs in tree-dwelling squirrels too.

Rabbits have a short white tail which isn't particularly camouflaged. It helps to confuse the predator allowing the rabbit to make sharp turns that the predator cannot anticipate.

In the case of this big bushy "twitchy" tail (which like rabbits, some squirrel tails have white tips, like in your picture), a predator probably cannot see the body and importantly cannot see or is distracted from the footing and pacing of the squirrel. If you've ever seen a dog chase a squirrel, the squirrel is easily able to outmanoeuvre the dog long enough to make it safely to a tree, probably because the dog can't predict the squirrel's trajectory due to the distracting and writhing tail.

Let's say a predator did get its jaws or claws near the squirrel and tried to take a chunk. There is a good chance all the predator will grasp is a bunch of tail fur. The squirrel will probably be sore but will live to tell the tail. (I couldn't resist)