Why would you move rook to H4?

Game: http://en.lichess.org/bgOyS4RO/black#0

Move #16 for black.

FEN: r3k2r/pppn4/3qpp2/3p2p1/1P1N2P1/2PQ4/P1P2P1P/R4RK1 w kq - 4 17

Why would this be a mistake? I was going for checkmate obviously... but I went through the 'orange' text... but I don't get why you would want to do that. Is it really force white to play Rook to e5? (15... Bh4 17. Qg3 O-O-O 18. Rae1 Ke5 19. Rxe5 fxe5)

18. ... Ne5 threatens Rxg4 winning the white queen and there is no satisfactionary defense for white. 19. f3/h3 fail to Rd/h8 pressuring h2 and white cant respond with rf2 after f3 because Rh3 is winning the queen.
After your move Qd6 white has Qg3+ (which he played) and now black has to move his king to the backrow and cant double on the h file anymore. (still slight advantage, but not that decisive). note that exchanging queens wont help, since white will lose either g4 or h2 and is a pawn down in a worse position.

enemiesofreason, thanks for the explanation. Helps a lot