what is it about the one key that makes it more secure than the one password for any online account?
legit curious here.
A bitcoin key needs to be generated mathematically, and is typically done from a strong random source.
Passwords, in general, are extremely non-random and are also much shorter than a bitcoin key.
A bitcoin key is 256 bits, generated in a near true random fashion.
A randomly generated password using mixed case, numbers and symbols would need to be over 40 characters long to have the same level of security.
This weakness in human generated passwords can be exploited by the use of dictionary attacks, and the building of dictionaries and rainbow tables. A web site needs to hold some data that allows it to identify the correct password (hopefully, this is not the password itself, or even an encrypted form), usually a "hash" of the password. Because there is only a relatively small pool of frequently used passwords, building a dictionary of passwords to probe into stolen "hashes" is feasible, and far more effective than you would expect, by just calculating the "entropy" of passwords.
Because bitcoin keys are randomly generated from a full 256 bit space, it is impossible to build a dictionary mapping public keys to private keys, because there are more bitcoin key-pairs than there are atoms in the universe. There are also so many possible key pairs that simply guessing is ridiculously unlikely to get you anywhere.
The direct computation of a private key from a public key is also impossible with current technology (if someone can build a real quantum computer, and make it run a quantum program called Shor's algorithm, it might be possible to do this calculation, but quantum computers of sufficient power are fairy-tale stuff at present).
To illustrate the problem with "non-random" sources, there HAVE been bitcoin thefts by "hackers" guessing private keys. These guesses have come from "brain wallets". A group of developers came up with a method of creating a bitcoin address that could be kept memorized. You would think up a short sentence, and use an algorithm to generate a bitcoin key pair and address. Entering that sentence into any "brain wallet" enabled bitcoin software would give you access to your bitcoins. The problem is that there is very little randomness in this, which makes building dictionaries of addresses and "pass phrases" possible. Early users of "brain wallets" who used "obvious" pass phrases have ended up with their coins stolen.
Private keys have also been "leaked" or "duplicated" by buggy software. E.g. the random number generator hardware/driver on some android phones was faulty, and the OS would have a tendency to generate the same sequence over and over, on each device. Some people were screwed because they generated a new address on a faulty android, and then someone else generated the same address and found the coins.