If you don't understand the sentiment, I recommend that you read about what happens in a "run on the bank". Too many large withdrawals at the same time results in a liquidity crisis. No bank in the country has enough reserves to pay all of its customer accounts at the same time; it's part of our system of fractional reserve banking. A massive spike in withdrawals forces a bank to sell long term securities in a disadvantageous environment, often for a huge loss. That undermines customer confidence and exacerbates the issue, causing more people to withdraw. A single person could bring the most successful bank to its knees in that environment, as long as enough customers believe them; it's a self-fulfilling prophecy.
https://en.wikipedia.org/wiki/Bank_run