In this YouTube video, the author says that 10...f6 "leads to disaster"...Why? Why is that at 10:44 of the video, 10...f6 leads to a disaster? 

https://youtu.be/BrbChWI89ek

 [FEN ""]

 1. e4 e5 2. Nf3 Nc6 3. Bc4 Nf6 4. d4 exd4 5. O-O Nxe4 6. Re1 d5 7. Bxd5 Qxd5 8. Nc3 Qa5 9. Nxe4 Be7 10. Bg5 f6?
The video's author might be overstating it by calling it a "disaster" as there is no clear knockout blow.

Nevertheless, white is clearly better, and the attack will continue with best play, but it requires accuracy or the extra piece may tell the final tale. White will remain down a piece for two pawns, and will probably win a third in the near future due to the indefensible black king. Here is a couple of sample lines, but since neither side is forced, there are many other possibilities.

 [FEN ""]

 1. e4 e5 2. Nf3 Nc6 3. Bc4 Nf6 4. d4 exd4 5. O-O Nxe4 6. Re1 d5 7. Bxd5 Qxd5 8. Nc3 Qa5 9. Nxe4 Be7 10. Bg5 f6 11. Nxf6+ gxf6 (11... Kf7 12. Ne4 {And white is not down any material, and the attack will continue. The black king is just too open.} Re8 13. Bxe7 (13. Nxd4 {Or this.} Bd7 14. Bd2 Qb6 15. Qh5+ Kg8 16. Nf3 {Idea Qd5+ and taking the Bd7.} Nb4 17. Neg5 Qg6 18. Qxg6 hxg6 19. Rxe7 Rxe7 20. Bxb4 $18) 13... Rxe7 14. Neg5+ Kg8 (14... Kf8 15. Rxe7 Nxe7 16. Nxh7+ Kg8 17. Nhg5 Bg4 18. Qxd4 Bxf3 19. Nxf3 Qd5 20. Qg4 $18) 15. Qd3 g6 16. Qc4+ Kf8 17. Rxe7 Kxe7 18. Qf7+ Kd8 19. Re1) 12. Bxf6 Rf8 13. Bxe7 Nxe7 14. Qxd4 Qb6 15. Qc3 Bf5 16. Rad1 Rd8 {This is clearly the best move here.} 17. Rxe7+ $1 Kxe7 18. Qe5+ Qe6 19. Qxc7+ Rd7 20. Qc5+ Rd6 21. Re1 Be4 22. Ng5 Qd5 23. Qe3 Qd4 24. Qxe4+ Qxe4 25. Nxe4 {And the position has finally clarified.}