This is a useful mnemonic, but is not the true origin of the terms. This term eventually was used to describe short sellers, speculators who sold shares that they did not own, bought after a price drop, and then delivered the shares. I.e., the bulls were those people who bought in the expectation that a stock price would rise, not fall. Both bull and bear markets are inevitable. Smart investors try to anticipate both events to profit from their eventuality.
Bear markets are generally shorter in duration than bull markets.
To avoid being hurt by bear markets you must recognize the signs early and move part of your assets into cash equivalent investments. We do recommend that you invest for the long term. The same thing is true of bears - don't panic and sell low. Let the bear market run its course, which history tells us is likely to be short. On the other hand, a bull market can leave many investors feeling pretty good about their ability to prosper.