For the most people, oil being down is a great thing because gas is lower, heating cost less, ect. Unfortunately, the market is not traded the way we think it should be traded
If we look at the DOW, there are 2 big companies that are oil majors. There is XOM and CVX in the DJIA. If they take a hit because of oil they bring down the DOW. The Dow is a key index so many stocks especially industrials go down in lockstep with this index.
That is part of the equation. The cause that made oil go down can also bring the general market down also. Consumers spending less, jobs loses, demand in Europe, and demand in China are all some of the things that will bring oil down and also bring the general market down. If you look today both CAT and BA are down because of woes of China.
Markets are traded around key levels like a $40 price on oil. The market does not like to be shocked or out of the norm. People buy and sell indexes which contain many stocks and so these trades bring the whole market down. This may bring other stocks down that should have no dependence on either the price of oil or demand of products from China.
The market is hard to predict and individual stocks can be up while others are down however, if we looked over a broad range of stocks they trade similar. I agree that oil prices being low are a boon to us and should be a boon to the rest of the market. The market, however, has its own mind and it behooves us to study the market and follow it instead of trading how we feel the market should trade.