This is never addressed directly in the original films - only in the lore that followed (and in particular the novels). There are ultimately three reasons why red lightsabers are predominantly used by the Sith:
- Red is a danger colour.
- Lucas wanted to distinguish between lightsabers rather than having them all the same colour.
- The backstory discussed in @Richard's answer.
@Richard's answer is of course correct and links to a detailed in universe explanation. Whilst I know you say you understand that the colour red distinguishes good from bad, I thought I would explore why that is in more detail as the in universe explanation has been tackled. Then, I'll look at behind the scenes of the Star Wars Universe and why the red light saber came to be used.
The colour red and its background of danger
Firstly, consider the trope of good colours versus bad colours. White and black have consistently been used to portray good and bad in films. A great example would be in Westerns, where the allegiance of a character could often be determined by their clothing.
Similarly, red and blue have often be presented as opposites. TV Tropes argue this could date all the way back to the War of Independence and the Americans (blue) versus the British (red). Even going beyond this (admittedly) controversial interpretation, red has frequently been seen as a "danger" colour. Consider a standard stop sign:
It is red, designed to gain attention and highlight danger. It's the colour of fire, something that humans have been wary of and respected for a long time. It frequently is associated with the Devil, and Hell, in religious ideologies. It has associations with power, for example consider the power red tie look*:
Whilst there is much research online about all this, to choose one example The Huffington Post released an article all about why red still makes us mad, concluding:
Red color did not just elicit a stronger physical reaction, but also a
faster and more consistently-strong reaction. This phenomenon is
similar to wild animal behavior where red may be seen as a color of
threat, inducing a rapid preparation for defense or flight.
How the red lightsaber came to be used in Star Wars
To quote from the Wiki on sith lightsabers:
Technically, the first Sith lightsaber designed was Darth Vader's.
However, there were no early plans to make Vader's weapon distinct
from the other lightsabers depicted, beyond the black styling on the
The original lightsaber effect was provided by the reflective,
spinning dowel that made up the blade, which appeared to glow to the
camera. However, Lucas was unsatisfied with these early effects, and
had the glows further augmented by rotoscoped animation. During this
phase, it was decided to make the lightsabers have different color
blades to further differentiate them, and Vader was given a red blade.
This is important to note as, to paraphrase from the wiki, it wasn't until Shadows of the Empire was released that any mention of internal crystals affecting light saber color was introduced.
*Yes, I'm aware I linked to Mitt Romney in an answer about the Sith. No, this was not indicative of any political views!
Just with regards to General Grievous, no he was not a Jedi/Sith.