Let's take Superman vs. Wolverine. Most agree that Superman would come out on top here using his full array of powers, so this isn't debunking a loss so much as a misconception. Most also would agree that Wolverine can cut Superman with his adamantium claws. This is the misconception, but of no fault of the claws. Adamantium is capable of piercing Superman's skin, but Wolverine is not strong enough to apply the pressure needed.
Say you are about to dig into overly frozen ice cream only to discover that you can't get a scoop out because the spoon won't go into your desert. Same principle—the spoon is strong enough to get through the ice cream, but you aren't. Superman can cut himself with Wolverine's claws, but Wolverine cannot.
Hows about Superman vs. Batman? Why must I read about these two characters facing off. One day Superman is being mind controlled by Brainiac, the next Batman is under Poison Ivey's influence, the next they both want Lois Lane. The worst part is Batman wins half the time.
I know the history, Superman gave Bats a green kryptonite ring in order to use against him in the event Supes went rogue. This is usually the ...