That's hardly symmetrical to the fear of losing the money that you have already invested – investors feel they have no choice but to sell before it gets worse, whereas in the rally you can always choose not to buy.
It's pretty symmetrical. Choosing not to buy is not as easy as it looks, when you are under pressure to do so. Madoff took advantage of this. The crash of 1929 was preceded by unhinged buying.
Even better: the percentage split between long and short holders isn't 50%/50%