Debit and Credit
Think of it this way, if you made money during the year, the net effect on your Assets would be an increase, or greater Debit balance. In order for the equation to work, this would mean that Equity would also have increased, or a greater Credit balance. In order for this to happen, Revenue would have to be a Credit, while Expenses would have to be a Debit. The resulting Revenue minus Expense would give you a Credit balance, or an increase in Equity. So Revenue is always a Credit, while Expenses are always Debits.
To go back to the what the bank is telling you, here is why they are right from their point of view. They owe you money (your bank account balance). This, to them, is a Liability. Therefore, any increase in the amount they owe you would be a Credit on their books. However, to you, your bank account is an Asset. Therefore, any increase in your bank account would be a Debit on your books.