I don't remember where I heard this theory from, but saying it anyway.

Pyrrha's Semblance was polarity, or magnetism. What do magnets do? Attract two opposites, and repel two likes.

Pyrrha was female, honest, kind, humble, athletically fit, and a prodigy.

Jaune was quirky, weak, often very blunt, couldn't take "no" for an answer, and cheated his way into Beacon.

Pyrrha's Semblance turns her hands black.

In "Forever Fall, part 2(?)" Jaune glowed white when Cardin was thrown off of him.

Jaune melted down Pyrrha'a armor and had it incorporated into his own.

It's not a stretch to believe that Jaune's Semblance is another form of magnetism, such as magnetic repulsion.