Why bullfighter capes are red

It's a classic trope, a bull will always run at flapping cape of red fabric. That's why bullfighters always use red capes right? At least, that's what cartoons taught us. But maybe the reason bulls charge has nothing to do with the color of the cape, and the red has a much more violent purpose. The following is a transcript of the video.

You've seen this before. The matador waves his red cape and the bull charges! What's the deal, bull? What do you have against the color red? A Matador's cape is called a muleta and they have a good, but gruesome reason for their color.
You see, bulls can't actually see red. Like all cattle, they're color blind to it. Then why the hate? Bulls are irritated by the movement of the cape. They see the waving fabric and charge, regardless of color. In fact, the muleta is only used in the final 3rd of a bullfight The matador uses it to hide his sword, and he pierces the bull as it charges past. The cape is traditionally red to mask the bloodstains. That's one way to save on dry cleaning.