I don't understand the logic behind HP

So, a brand new fighter can easily have 25 HP (15 Constitution + 10) but a Dragon only gets 16 HP.

I kind of get it that DW is trying to make levels less important, so that you don't have to be max level to go fight dragons, but even with Armor 5 isn't the dragon going to die really, really fast?

Or am I still too stuck in the rules & numbers mindset and I'm just not getting how to DM the dragon?

Have you read the 16 HP Dragon post on Sage's blog?

That's a great post, thank you for linking it.

It's sort of what I was assuming was the answer, but I'm still wrestling with the concept.  I mean, in the scenario just described, if everybody HAD rolled well to defy danger (against being terrified), and then the wizard HAD rolled some good damage...the dragon would have died really fast.

Yeah, I get it that it's the creative fiction that makes it work, but then I wonder: why bother with numbers and dice at all?

Numbers and dice are there to add uncertainty and excitement.
BUT, if you stay "behind" numbers, you lose that excitement quite fast.

I want to catch your problem (maybe so do you...). Is it

1) A truly epic combat MUST take a significant part of REAL TIME.
           In my experience AT THE TABLE, when a combat drags for more than 15 minutes. people start slipping out of fiction. So, I think it's best if you are able to save some time.

2) Heroes must be abel to do MORE cool thing before combat ends
           In a trad. game, if a combat lasts for, say 15 rounds, what is the game time, 5 minutes? If three heroes fight for 5 consecutive minutes with a dragon, a lot can happen. I don't remember if it's 5 minutes, but you get the idea.

3) An epic battle may last for DAYS (like Gandalf Vs the Balrog) because enemies are TOUGH! I don't want brittle enemies who die fast!
          Try to stretch combat time. You CAN do this; it's not against the rules.
You can describe HOURS of combat, standing at the gate, resisting, or chasing across the mountain top. Explain this to the players; say it can happen. It's not against your principles or agenda, describing three days of battle with an ancient monster. Just make sure it is honest and fantastic.

Just see 'HP' as mistake potential during combat or physical adversity. Its a measure of tension in the antagonism. Once they are whittled away, our heroes (or their foes) cannot handle any more mistakes without facing death's dark gates. So use the deal damage move ALL the time - as a soft move, as a hard move, as a fictionally appropriate move in addition to whatever else is happening.

Don't forget that on a player miss you get to make as hard a move as you'd like (don't hold back now).

I mean, in the scenario just described, if everybody HAD rolled well to defy danger (against being terrified), and then the wizard HAD rolled some good damage...the dragon would have died really fast.

You mean like the way Smaug died when Bard shot him with the Black Arrow?