If you have money deposited where you also owe money, you might find that your deposited money is gone. I wrote over a year ago about how if you file bankruptcy, a place where you owe money might take the money you also have deposited there (article), but it doesn't necessarily take filing bankruptcy to trigger that result. If you're delinquent on a credit card debt, that credit-card bank may take the money owed from any deposits you also have with that bank without waiting for you to file bankruptcy. It's called a "right of set-off" and is a complex subject; the simple version is don't let yourself get caught by it.
But, you say, I'm current on my ABC Bank credit card; so what's wrong with also having money deposited with ABC Bank? Do you know that you'll always be current with that credit card? Do you know you won't get delinquent for some reason and, by that time, forget that you also have money deposited there. Do you want to take the risk?
It can get trickier than that. You have a deposit account at a branch of DEF Bank; you don't have any DEF Bank credit cards. Surprise! One day you find that your money is gone from that account. What happened? You have a delinquent credit card account with GHI Bank and some point GHI Bank was bought by or merged with DEF Bank. Bingo, DEF and GHI are the same bank and your money is gone. So be very careful out there.