Why ARE there brilliant moves in chess?

@tpr said ^

• That is why a true brilliant move is a quiet move, no check or capture. Those are too obvious.

1. Fischer played Nxf2 against Robert Byrne which is considered brilliant.
2. That move is a capture.
3. Therefore a 'true brilliant move' can be a capture.

Q.E.D.

Not brilliant to me.
Neither is the Greek Gift Sacrifice Bxh7+.

@tpr said ^

A true brilliant move satisfies 4 criteria
note necessarily, it isnt the ONLY move that wins.

@tpr said ^

4. It is a quiet move: no check or capture.

Chess.com clearly disagrees with you on that one, while it is a possibility for a quiet move to be brilliant it doesn't necessarily mean its a requirement.

"Chess.com"

• This is not Chess.com.
  For a real brilliant move it is a requirement.
  Likewise in problem chess a key move is always a quiet move.
  Checks and captures are too obvious.

One persons Brilliant move is the Other mans free material

@tpr said ^

A true brilliant move satisfies 4 criteria

1. It is a move that wins.
2. It is the only move than wins.
3. It involves a sacrifice.
4. It is a quiet move: no check or capture.

it is not necesary

"It involves a sacrifice", but...
"It is a quiet move: no check or capture"

Could you clarify?

"Could you clarify?"
Here is an example of a true brilliant move: 30 Ba3
It wins
It is the only move that wins
It involves a sacrifice
It is a quiet move
https://www.chessgames.com/perl/chessgame?gid=1031957

Okay, it satisfies your criteria, but brilliant is still relative. It is only your opinion (not a fact) that a brilliant move must be quiet and not a capture or check.