Is Bobby Fischer hanging a knight? So I've been looking at the "Game of the Century" between Bobby Fischer and Donald Byrne. There's something I can't get over.

In move 18, that queen is tempting, but there's also a knight on c3 that is not immediately protected.

[Title "That knight on c3 appears to be hanging"]
[fen "r3r1k1/pp3pbp/1qp1b1p1/2B5/2BP4/Q1n2N2/P4PPP/3R1K1R w - - 0 1"]


Is there a reason, which I don't see, why White shouldn't just take the knight here? It seems to me that this takes the wind out of the sails of most of Black's attacks. It appears Black has no good way to recover, as Black still has to move his queen or lose it and the knight. And there's suddenly not a lot of good spaces to move it to either.
I would not normally answer this question since the other answer points out the basis for the first move of the variation, but only the first move. It left out why white is so lost in that variation, and why Byrne did not play it.

At the end of both lines below, there are written notes explaining the resulting position.

 [Event "New York Rosenwald-03"]
 [Site "New York"]
 [Date "1956.10.17"]
 [Round "8"]
 [White "Byrne, Donald"]
 [Black "Fischer, Robert James"]
 [Result "0-1"]
 [ECO "D97"]
 [PlyCount "82"]
 [EventDate "1956.10.07"]
 [EventType "tourn"]
 [EventRounds "11"]
 [EventCountry "USA"]
 [FEN ""]

 1. Nf3 Nf6 2. c4 g6 3. Nc3 Bg7 4. d4 O-O 5. Bf4 d5 6. Qb3 dxc4 7. Qxc4 c6 8. e4 Nbd7 9. Rd1 Nb6 10. Qc5 Bg4 11. Bg5 Na4 12. Qa3 Nxc3 13. bxc3 Nxe4 14. Bxe7 Qb6 15. Bc4 Nxc3 16. Bc5 Rfe8+ 17. Kf1 Be6 18. Bxb6 (18. Qxc3 Qxc5 19. dxc5 (19. Rc1 Bxc4+ 20. Qxc4 Qf5 {And in this position, it is particularly hard to get the white king out because g3 is impossible due to Qxf3 (and if it moves or becomes defended, then Qh3 sealing in the Rh1), and again white is down a pawn with the worse minor piece, d4 is weak, and white is behind in development with a weak king. That the queens did not come off exacerbate that issue.}) 19... Bxc3 20. Bxe6 Rxe6 {And white is lost because he is down a pawn, the black bishop is much better than the white knight, both a2 and especially c5 are weak, and white is behind in development and has to deal with getting the Rh1 out. One more thing that would probably come into play also is that with the dark-squared bishop, f2 is particularly vulnerable too.}) 18... Bxc4+ 19. Kg1 Ne2+ 20. Kf1 Nxd4+ 21. Kg1 Ne2+ 22. Kf1 Nc3+ 23. Kg1 axb6 24. Qb4 Ra4 25. Qxb6 Nxd1 26. h3 Rxa2 27. Kh2 Nxf2 28. Re1 Rxe1 29. Qd8+ Bf8 30. Nxe1 Bd5 31. Nf3 Ne4 32. Qb8 b5 33. h4 h5 34. Ne5 Kg7 35. Kg1 Bc5+ 36. Kf1 Ng3+ 37. Ke1 Bb4+ 38. Kd1 Bb3+ 39. Kc1 Ne2+ 40. Kb1 Nc3+ 41. Kc1 Rc2# 0-1