It's definitely an incredibly awkward line. Which ever the meaning Square meant to convey they could have done it a hell of a lot better than that lol!
But originally I thought Cloud was talking about himself. His journey did begin there if you think about it. Yes his head was messed up and there were countless other places that could be represented as the beginning of his journey but it's where he wakes up from the mako poisoning in a 1st class soldier outfit, acquired the Buster Sword and became Zack's living legacy.
I also thought it was supposed to be a positive and encouraging line for Denzel whom he brought up there as if to say "Yeah I became a hero even though I woke up here to find my best friend dying trying to protect our freedom and even though I wasn't in my right mind I went on to try and save the world etc." kinda thing. Sorry for the awkward phrasing XD Also could it have been there to mirror the Angeal-Zack, then Zack-Cloud relationship? The way they looked up to their predecessor? Denzel looked up to CLoud the same way.
THEN On the other hand...
Was he talking about Zack? Never originally crossed my mind but after reading these posts....I'm not sure. :L As ye said before it could be a reference to Zack and his "Do you think I became a hero?" line. But as also pointed out before Zack's journey as a hero began long before that - with many debatable starting points. So I think it's a little more likely to be carried onto Cloud (the hero line in the end of C.C). Zack was most definitely a hero and Cloud wanted to be one too.
So there you have it. In my opinion Cloud was talking about himself. And even though it does sound arrogant considering what happened there I don't think it was meant to be. It's just an awkward line.