Here's why:
* Spectator comes from the Latin word "spectare", which means "to look at" or "to behold".
* Spec- is the root of "spectare" and carries the meaning of "seeing" or "looking".
You can see this prefix in other words like:
* Spectacle (a public display or performance)
* Inspection (the act of examining something closely)
* Perspective (a point of view)
* Spectacles (eyeglasses)