It makes perfect sense! Cations, you see, are attracted to anions. And reduced by cathodes. Anions? Attracted to cations. And oxidized by anodes.

Whereas cations are oxidized by anions, and anions are reduced by cations.

The only alternative here would be if cathodes and cations were positively charged, and anodes and anions were negatively charged. But then cathodes would reduce anions, and cations would also reduce anions. Even worse, anodes would oxidize cations, and anions would also oxidize cations.

And we can't have that. It would just be too confusing.