I believe that the previous answer misunderstands the meaning of the quote.

The meaning is that banks are more willing to loan money to those who do not need it as badly, at times when they do not need it as badly.  Banks are less willing to lend during bad times or to people who really need the money.

It makes sense that banks would be this way.  They do not want to lose money making bad loans.  Therefore, the are more willing to lend to companies during good times when those companies are likely to make money and pay them back.  They are more willing to lend to people with money who are, again, more likely to pay them back.

By contrast, when times are bad and companies really need the money, banks will be reluctant to lend.  This makes sense because they do not want to lend money to a firm when demand has gone down and the firm might not be able to repay the loan.

In this way, it can seem that banks only lend the umbrella (money) when it is sunny (good economic times).

This is a funny sentence. It is basically saying that banks offer things to you that you do not need and when you need something, they take it away. I can see from where this person is coming. Let me offer three points. 

First, it would be nice for the interest rate to be higher in our savings account. We get nothing for saving. Is not saving a good thing? If a nation hurts is savers and bails out those who have a spending problem, we are hurting the nation at its core. 

Second, banks make bad loans for the sake of profit and they now want hard working tax payers to bail them out. We are covering for their mistakes.

Third, if the problem of banks is that they are too big to fail, then why are they now bigger? It's pour out there and the banks have taken away our umbrella.