This. (And perhaps more specifically, in this context: fear is more widely and more quickly self-reinforcing, self-perpetuating and self-compounding, at a "societal-trading level" than greed is.)
^ That may be but crashes happen because of the absence of liquidity. Speculative bubbles, or blow-off tops, is as close as the market gets to a 'flash rally'.
Notwithstanding the facts you omit: There are more 'longs' than 'shorts' in the market. When the longs panic sell, the move is 'stronger' than when the shorts panic buy.
Typically they move at a very different rate from that of "flash crashes", though, I think? Not in the same way, to the same extent, or at the same rate as traders who are long, no; and maybe there aren't as many of them, either. (I may be saying the same thing as Userque, above, just in slightly different words, though, so I'll stop there.)
I think generally ‘potential energy’ of the market is far greater to the downside simply because the value of speculative capital positioned to the long side is many times that of what is short or ‘sitting on the sidelines’ ready to be deployed. OP is specifically talking about the broad stock market. Individual names or commodities are obviously different animals, so to speak.