[thirsteh]

Well, the difference is that if I compromise any of the sites you use, I now know all your passwords. If I compromise any of the sites you use when you use a password manager properly, I'll only know one password that'll be fairly useless to me.

[aba_sababa]

Compromising one of these passwords does not at all mean that all the other passwords are compromised. You can't figure out the original master password from a hashed, compromised password.

[thirsteh]

Yes, you can. To understand why, compare:

This:

  'facebook' + 'mypassword'
  'twitter' + 'mypassword'
  'foursquare' + 'mypassword'

Password manager with unique passwords:

  'mSX32ZyKZXptY3E'
  '33RiKbc3n6sA6IY'
  '4kGzFtWDd0rnti6'

All I have to do is figure out what you named the site that I compromised, then do exactly what I'd usually do to recover your password, and, voila, I can now access all sites you use it for. Compare this to the password manager example where each password has been generated at random--one password communicates no information whatsoever about the other.

[aba_sababa]

Ok, so you know that "facebook" is part of the original hash. Not following how you can also derive "mypassword" from it. If you have a good strong master password, rainbow tables won't be able to crack the hash.