I was struck watching our local squirrels as to why their tails were so large in comparison to their bodies. No other climbing animal seems to need such a large appendix, so is it for balance, warmth, food reserve or sexual display?
I’ve long suspected it was a decoy and distraction.
Most of that tail is hair. When a cat strikes at the squirrel, it’s as likely to strike the tail as the rest of the squirrel – it’s as long as the rest of its body. Even if it strikes the tail, the cat will most likely get air, rather than flesh-and-blood tail.
The way the squirrel moves shows that it intends the tail to be a decoy. Watch the way it moves when they run/hop. Or the way they’ll jiggle their tail (and nothing else) when trying to capture a cat’s attention.
So my vote – squirrels got long tails because the long-tailed ones (especially those who used it for deception) lived long enough to reproduce.
Certainly they use it for balance (using it as a ‘paddle’ to push against air resistance in the same way as a tightrope walker might use an umbrella), although that may not be the only reason;
Another thing; when they make long flying leaps from one tree to another, their tails help to maintain the correct attitude.
And having the right attitude is half the battle 
WEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEE!