Why was the cold war a war no one could win?

The statement is incorrect; Ronald Reagan won the cold war. The key is to prevent the war from becoming "hot"; to prevail against the enemy without actual combat.

The key to Reagan's victory was in forcing the Soviet Union to spend so much money on the military that the rest of the economy would collapse, and this is pretty much what happened. His "Strategic Defense" initiative, pejoratively named "Star Wars", would have provided some defense against ballistic missiles. An ABM (Anti-Ballistic Missile) system doesn't have to be perfect; it simply needs to increase the level of uncertainty that a Soviet first strike would have destroyed the US missile force. Between this and the intermediate range missiles deployed to Europe, and Soviets were unable to afford enough offensive ability to destroy it all. The Soviets tried - and collapsed their economy. The Soviet Union disintegrated. We won the cold war.