in calling for the Navy to "blow up the well" in the Gulf of Mexico that is gushing oil.
I think I've figured out why people might think that this is a solution. They see that there is a path (the well) from the reservoir to the surface. Take away that path, they reason, and the gusher will stop.
But that path is only part of the problem. Oil accumulates underground because it reaches an impermeable layer of rock. Oil is lighter than water and rock, so it tends to migrate upward. The problem that is not solved by "blowing up the well" is the breach in that impermeable layer, also the well.
Explosives won't seal that breach. They will fracture a lot of rock and break up the path to the surface so that it will be tortuous rather than the relatively straight and potentially more controllable wellbore. They may even fracture the impermeable layer still further. The result could well be multiple seeps or even blowouts with no means of control other than drawing down the reservoir. Which will take a lot more time than drilling relief wells.