If oil prices fall because supply was increased too much, then demand will increase in response to the lower prices of oil.

Petroleum fuels are only the only game in town for some of their applications. For everything else, raising or lowering the price relative to the alternatives will cause switching to or from petroleum fuels. This is going to be lagging (because there are usually capital costs associated with the switch, so it doesn't make sense to switch if you won't recoup the expense, so the fuel cost difference needs to be substantial), complex (because the switching will actually be based on the perceived future price difference, not the current price difference) and somewhat sticky.