Suppose that you see Linda go to the bank every single day. Presumably this supports the hypothesis H = Linda is a banker. But this also supports the hypothesis H = Linda is a Banker and Linda is a librarian. By logical consequence, this should increase my credence in the hypothesis H = Linda is a librarian.
Note that by the same logic, this also supports the hypothesis H = Linda is a banker and not a librarian. Thus, this should increase my credence in the hypothesis H = Linda is not a librarian since it is directly implied by the former.
But this is a contradiction. You cannot increase your credence both in a position and the consequent. How does one resolve this?
Bayesianism is about shifting probabilities. It might help to have a full blown example.
We have a society with 1000 people. 50 of them (5%) are Bankers. 50 of them (5%) are librarians. 1 of them (0.1%) is a librarian and banker (1 of the existing 50 listed before, not a new one).
I have a person behind a closed door. Knowing nothing about this person, you can assume a 5% chance they're a banker, a 5% change they're a librarian, and a 0.1% chance that they're a librarian and a banker.
Now, I tell you this: the person behind the door is a banker. How do those probabilities change?
Your space of possible people shrunk by 950 people - there's 950 people you know this person isn't.
You now know there's a 100% chance that they're a banker - so that probability went up from 5% to 100%.
You know there's a 2% chance they're a librarian - because 1 of the 50 bankers are librarians - so that probability went down from 5% to 2%.
You know there's ALSO a 2% chance they're a librarian and a banker - this probability went up from 0.1% to 2%.
This is how learning they're a banker can be evidence against them being a librarian, but evidence for them being a banker-and-librarian.