You might have noticed, that in the Arabic language, the word "left" is metaphorically used for something bad or impure. And the other way around for the word "right".
The word right:
69:19 - 69:21
So as for he who is given his record in his right hand, he will say, "Here, read my record!
Indeed, I was certain that I would be meeting my account."
So he will be in a pleasant life -
And the word left:
69:25
But as for he who is given his record in his left hand, he will say, "Oh, I wish I had not been given my record
Now there are plenty of examples in the Quran mentioning this. It's also mentioned in the Hadiths. For instance, there are the hadiths one sleeping on the right side as a good Sunnah, and also eating with the right hand.
Eating with the right hand is more focused on because, the left hand is used for more impure actions, therefore the right hand is more pure to eat with.
If we look at other languages we will also find out that the same concept is used, and it's a rather old concept.
What I wonder is, where the origin of the concept of these words has come from? Somehow the human derived to believe that the right is good and the left is bad, while these are just words we define and understand in our way of life.
The question might be more a question of language and not of religion. But the words are surely used in the Arabic language, thus in the Quran.
It might be that nobody really have a real answer on the question.
Also, it is known that the majority of the people are right handed. This has sometimes been the argument of why "right" is considered to be good. But it's not possible to know if the majority of the people really was right handed BEFORE the concept of that right meant something good. So the argument is not truly valid.
Edit: I noticed votes for closing this question. This question might look like having nothing to do with Islam. But if you take a look at the terms of left and right you will notice that many of the Muslims today include these terms in their theology, without explaining the origin of the terms. This question is an attempt to get an explanation of the origin of the terms that many surely use in Islam.