Why do squirrels have twitchy bushy tails?
Tree jumping.
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.
A big bushy tail might be a good counter to predation.
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 &quot;twitchy&quot; 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)