Why does a trial balance still tally even when there are errors?

A trial balance only checks that total debits equal total credits, so some errors do not affect agreement. These are called errors not disclosed by the trial balance. The main ones are: errors of omission (a transaction completely left out), errors of commission where a wrong but equal amount is posted to both sides, errors of principle (treating a capital expense as revenue), recording in the wrong account of the same class, and compensating errors where one mistake cancels another. For example, if you forget to record a sale entirely, both debit and credit are missing equally, so the trial balance still tallies. That is why a matched trial balance is necessary but not sufficient proof of accuracy. Rectification and a proper audit are still needed to catch these.