GL out of balance - what can cause it

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I continue to be baffled by the things that can happen in Sage.  I have never worked in an accounting system before where the GL could go out of balance.  If I enter a check, for example, the check amount must equal whatever expense accounts or AP" amounts that apply to it.  If I make a deposit, all individual components must have balanced credits and debits for enter the transaction.  If every single transaction balances, how can the GL ever get out of balance?  What could I possibly get Sage to accept where the debits and credits did not balance?  Or where the cash did not balance to what it should be?

Someone please help me to understand this.  I have taken my share of accounting classes and in an era where we learned to begin with a general journal and post everything by hand and the spread through other journals from there.  My point is that I should be able to understand any reasonable answer.  I work for a CPA and he seems to understand it, but is completely incapable of explaining it.  He just tells me to keep looking through entries until I find it.  I don't even have a clue what I am looking for.