Why not expand this argument to the general public? If the airlines charge more than I think I ought to pay, why don't I just start my own coop airline? Once my family, my co-op partners, and I have done all the flying we want to do, we could sell the extra seats on the open market.
First off, you are assuming that there are refineries for sale in this country. There aren't. Why would Shell, or ExxonMobil, or Chevron sell off a part of the company that is like a license to print money?
Building your own refinery is not a solution either. You are looking at an upfront cost of several billion (that's billion with a capital "b") dollars. There is a reason why the major oil companies who have that kind of money have not built a new refinery in this country in over 20 years. In fact, under pressure from environmental laws, the oil companies have closed and walked away from a number of smaller refineries over the past 20 years rather than make the changes necessary to reduce the pollution emitted from those less efficient refineries.
Finally, there is your price/production argument. "If oil prices rise, production increases, and the co-op would keep member costs down through profits from the open market sales." The reason oil prices rise is due to a shortage (real or artificially induced) of crude oil. Every refinery needs crude oil inputs at the front end in order to produce jet-A, or gasoline, or whatever on the back end. You can not increase production if you have a shortage of raw materials.
Storing excess supplies of crude oil when prices are low does not work. A tank farm has an enormous "footprint." It takes a lot of land which is in short supply on the coasts of this country. The oil companies were among the first to do "just in time" manufacturing. Oil tankers are scheduled into a berth at the refinery shortly before the crude oil on board is needed. The storage for the crude oil is the ship itself.
And there are those pesky environmental laws passed by Communists (obviously, since the laws require the oil companies to spend money they don't want to spend) whose constituents were tired of bad smells, and headaches from the fumes, and higher incidences of cancer among neighborhoods near almost any facility having to do with the oil bidness. Almost everyone agrees that we need more refineries in this country. The problem is that everyone thinks that refinery should be in your backyard, not theirs. Even conservatives feel that way. Case in point...people in Florida see no problem whatsoever with oil/gas drilling in the Gulf of Mexico off the coast of Texas, Louisiana, Mississippi, and Alabama. However, they (and their governor and his brother, the Prez) think that there should be NO oil/gas drilling off the coast of Florida. The area is too environmentally sensitive, don't you know.