No, it is symmetric. Your confusing point of few with symmetry.
Why both Kings are on the right when starting a game?

Nope, no symmetry. If you're playing as White your King it's the fourth from your right, if you're playing as Black your King it's the FIFTH from your right.
They are both symmetry by "center" or "axis". However, one told me that if black's queen faces the white king, then d4 and e5 will be two strong pawn which can beat each other, and after exchange one of the queens will dominate the center with open file against the opponent's king and then castle to the different side and put pawns ahead to enlarge that advantage. The chess will fall into such an easy game like that。

Symmetric as in in front of us (so kings in front of each other, 6 squares away), it is proper, because kingside refers to the king pawns and it would be akward if black castled on the other side.

if black's queen faces the white king, then d4 and e5 will be two strong pawn which can beat each other, and after exchange one of the queens will dominate the center with open file against the opponent's king and then castle to the different side and put pawns ahead to enlarge that advantage. The chess will fall into such an easy game like that。
Oh thanks, I didn't think of this.

Your opponent's pieces appear as your would in a mirror. That is symmetry, as opposed to rotational translation.
By the way, I've tried a flipped black king/queen variation a few times with a friend. It doesn't play very well in my opinion.

Your opponent's pieces appear as your would in a mirror. That is symmetry, as opposed to rotational translation.
Yeah, of course you're right, along with Wouter_Remmerswaal. I just meant rotational symmetry, not reflection symmetry.
Anyway I got your point, the game gets awkard if both kings face queens. :)
Hello there! I've just learned playing chess and I noticed that when starting a game both Kings are on the right and both Queens are on the left (for the White player as a viewer).
Why there is no symmetry in the positions of Kings and Queens? Is there some kind of advantage from this setting for one of the two players?
Thanks