Double edged sword vs single edge
"Double-edged sword", as a metaphor, has always been linked with "cuts both ways", meaning it can (figuratively) hurt both the person attacked and the attacker.
In European tradition, swords are made with double edged. In Japanese tradition, however, a sword like a katana is a single edged blade. What advantages/disadvantages does a double-edge sword have over a single-edge?
The double-edge sword can cut upwards faster and easier, especially after a downward cut, and this is one big advantage. A single edged blade will often make that edge a bit better at cutting. This isn’t to say that a double edged blade can’t be good at cutting. There were blade designs that attempted to mimic the curve possible with a single edged blade in a double edged blade.
Whether a sword is single-edged or double-edged has very little to do with how well it can be used for a thrust. The bigger considerations are the shape of the tip and the alignment between the tip and the handle. The Katana would be one of the best single edged weapons. It is a slightly curved, single-edged sword used for light cuts and deep thrusts. The alignment of a katana between the tip and the handle is straight enough to make for a very efficient thrust. The mune of a katana is more durable for doing deflections.
The advantages of any weapon depend entirely on the circumstances for which it is designed. Each type of blade is designed to be better under different fighting styles. A single edged sword is designed under fighting styles that utilizes more slashing and slicing attacks. Double edged blades were developed for fighting styles that took advantage of having two sharp edges. Each has their advantages and disadvantages, but the fighting styles used for each takes advantage of their pro's, and minimizes their con's.