The cardinal is protecting its territory from the bird in the window. Really. He will stop this silly behavior once his mate's chicks hatch and he will have to do real-world work like feeding them.

In the meantime, dangle something (aluminum pie plate) outside the window so it breaks up the reflection.

Soon you'll have baby cardinals in the yard hopefully not as goofy as their dad!

I had a robin doing the same thing for years. I found I had to eliminate the entire reflective surface of the window (he just started fighting with another area away from dangler)by tacking a piece of landscape fabric over the window on the outside. It's not as ugly as you might think and it worked!

A bright light shining out of the window also prevents reflection.

Paul