"It's pretty intuitive and I'm sure you know it: People being able to break the rules. Eg: create coins out of nowhere..."

Ah, but therein lies the problem. If there is no authority that issues the money, then any party must be able to create money from nothing (or there would be no money in the system), and must be able to do so efficiently. This is where the first vague notion of security in Bitcoin arises: the idea that you can generate the money efficiently, but not "too efficiently." Unfortunately there is no well-understood security model that allows for efficient-but-not-too-efficient attacks.

"Don't you agree that Bitcoin involves too many disciplines to try to simplify it into a cryptographic formula?"

Two disciplines, as far as I can tell: economics and cryptography. One discipline motivates the other here. Theoretical understandings of money and money creation come from economics; whatever that understanding is, the security definition needs to capture it. The involvement of another discipline does more to motivate the demand for a security definition than to make it irrelevant.

Suppose you could identify or develop an economic theory for money that has no intrinsic value and no central authority. You would still have to have some security definition that captures that theory to make a convincing case (or at least a meaningful statement) that the money in Bitcoin meets the requirements of that theory. If you cannot identify an economic theory that supports a system like Bitcoin, you are no better off than if you cannot state a rigorous security definition.

"Something that breaks Bitcoin could even simply come from Economics, and your crypto model (if you ever find one) would be useless."

Whatever hypothetical security definition you had would not be useless in that case. Rather, it would be that systems that satisfy that definition do not make economic sense, and hence that entire category of systems has no practical use. I would say that in that case, Bitcoin would be solving the wrong problem, rather than that Bitcoin was "broken" (which I take to mean that it does not solve the problem it is supposed to solve).

"Let's try with an analogy (you can attack it or say why it's bad). Your ship is sinking for some reason, there are no emergency boats, but you find out something that might be used to stay afloat."

Are you suggesting that Bitcoin is a system that people desperately cling to when they believe that well-designed systems are failing? I think this might be the wrong analogy, at least if you are trying to defend Bitcoin.

A better analogy might be this: you are standing on a ship. You do not like the captain and his decisions, so you grab some hunks of wood, styrofoam, tires, and a barrel full of fuel oil, lash it together with some rope, and set sail.

Which would you rather be standing on -- a well-engineered ship that might sink if the captain makes bad choices or if the crew fails to maintain it properly, or something that some guy assembled from stuff he found that seemed relevant to ship-building and which seems to float, seems to have no captain to make bad decisions (but might be split in half if the crew cannot agree on a heading), and which has not yet sunk under the weight of its passengers?

"If by breaking Bitcoin you can silently steal millions and safely cash out (one hell of an incentive in my book), yet no one does it, I say it's secure enough. Not in a cryptographic or <individual traditional field> way, but in a pragmatic way. It just works."

What if the attacker does not want to steal money, but just wants to disrupt the system? Imagine a hypothetical "Satoshiland" where Bitcoin is a major economic force; now imagine that another, more powerful country is about to go to war with Satoshiland, and that their goal is to destroy everything. If the invader can block transactions, create transactions then reverse them, and kill the mining bonus, they can cause vast economic harm -- without firing a single gunshot.

Or (slightly) more realistically, what if the US government wanted to block payments to Wikileaks. What if that is worth more than whatever it costs to do so (ie a "51% attack"), and more than whatever hypothetical mining payoff could be had by just devoting the hardware to mining?

I would not assume that the adversary's goal is your personal goal.