Bad symmetrical variations I know that symmetrical variations of some openings are good up to a certain point, after which White gets a significant advantage (like gaining a piece or even mating the opponent's king). One such example is the match below, following the Italian variation of the Four Knights Game (C50):

[Event "?"]
[Site "?"]
[Date "?"]
[Eventdate "?"]
[Round "?"]
[Result "1-0"]
[White "NN"]
[Black "NN"]
[ECO "C50"]
[WhiteElo "?"]
[BlackElo "?"]
[Plycount "27"]
[FEN "rnbqkbnr/pppppppp/8/8/8/8/PPPPPPPP/RNBQKBNR w KQkq - 0 1"]

1.e4 e5 2.Nf3 Nf6 3.Nc3 Nc6 4.Bc4 Bc5 5.O-O O-O 6.d3 d6 7.Bg5 Bg4 8.Nd5 Nd4 9.Qd2 Qd7 10.Bxf6 Bxf3 11.Ne7+ Kh8 12.Bxg7+ Kxg7 13.Qg5+ Kh8 14.Qf6#
1-0


After the move 9. ..Qd7, White gains a significant advantage in which Black will have to sacrifice some pieces (even the queen in one line) or he is getting checkmated.

My question is: do you know any other example of situations like this, where White gets a significant advantage after a few moves performed in a symmetrical fashion?
From the OP and the discussion in comments I guess you're looking for more nuanced variations. Here's one that comes to mind from the Queen's pawn game (symmetric-pseudo-Catalan), where if black doesn't break the symmetry at some point, white will either be up a pawn or have tangible positional advantage. 

 [title "Queen's pawn game example"]
 [fen ""]

 1. d4 d5 2. Nf3 Nf6 3. g3 g6 4. Bg2 Bg7 5. O-O O-O 6. b3 b6 7. Bb2 Bb7 8. Nbd2 Nbd7 9. c4 c5 10. e3 e6 11. Ne5 Ne4 12. Nxe4 {Here black can no longer keep playing symmetrically, as exemplified in the shown mainline. Instead black has to simply recapture on e4 and it's a normal game.} Nxe5 (12...dxe4 {optimal continuation for black here, breaking the symmetry.} 13. Nxd7 Qxd7 14. Qc2) 13. dxe5 dxe4 14. Qc2 Rb8 (14...Qc7 15. Bxe4 {and white is up a clear pawn}) 15. Rad1 Qc7 16. Bxe4 Bxe5 17. Bxe5 Qxe5 18. Bxb7 Rxb7 {despite the symmetric pawn structure and equal material, white has a clear positional advantage as they control the only open file and black's disconnected rooks are far from being in time to challenge the file.}