Why the trial balance may not balance?

Answer:The purpose of the trial balance is (historically) to verify if any errors were made with posting the journal entries to the ledger. Every journal entry makes debits and credits to (at least) two T-accounts, where the total of the debit and credit amounts need to be equal. The journal entry is posted to the journal, and the T-accounts affected are updated in the ledger.

The trial balance is a list of all T-accounts and their balances. As the underlying journal entries need to balance out (total debits equal total credits), the balances of the trial balance also need to balance. If this is not the case, it means that an error has been made. It means that some journal entry has been entered into the ledger which did not balance.

With computerized bookkeeping, this purpose (checking for errors) has been lost (at least for the user, the software may still use the trial balance to check for consistency).