Am I overconfident (or is this really a draw)?

Just played a 45/45-game on ICC. At move #19 my opponent offered me a draw. I declined. He offered it again two more times shortly after. We kept playing, and he blundered a Knight away, and resigned.

To me, the White position is clearly better at move #19. So, my question is: Am I overconfident about my position, or is there something I'm completely missing? 

Here's the game: 

At move 12, white isn't down a knight, just up a pawn.

And the position is obviously drawn. Rxh4 1-0

If only Re1# were possible

Thank you for the correction regarding move #12. 

This I don't understand: "And the position is obviously drawn. Rxh4 1-0" - you say the position is a drawn position, and you say 20. Rxh4 wins. So, what is it? A draw or a win? 

Yes, there is no checkmate. That's why I moved my Knight out. I could also have captured the Knight, but I wanted my pieces in play. 

 I deleted my comment almost immediately after I posted it.  When positions are posted they usually indicate "White to play" or "Black to play".  Didn't look at the game notation closely enough before posting. 

I see. 

at move 19 white is probably objectivly winning. 

1)black king is strangly placed and will have a hard time getting his  queen side pieces in the game, and protecting his king,if he ever can do those things at all.

2) White has a protected passed pawn (after white playes g5 which he should definatly do next move if possible.)

actually #2 is what should win the game for white.