Why does the battery show a negative voltage when tested with a voltmeter?

This can happen for a variety of reasons, including:

You may have measured incorrectly. Ensure that the plus and minus poles are measured with the voltmeter's corresponding measuring ends. There will be a negative voltage if they are switched.
If the poles of your voltmeter are connected correctly, there is a possibility that the battery suffered a phenomenon called "polarity reversal". This is a rare occurrence that can happen at the end of a discharge with two or more batteries connected in series.
When battery A (high electrical capacity; not yet depleted) and battery B (low electrical capacity; nearly depleted) are discharged in series, battery A retains a significant amount of capacity while battery B is near depletion. When this occurs, it is possible that battery B will be discharged further by forced current from battery A. There is a chance that battery B will receive a negative voltage in this case. This can occur when old and new batteries are mixed together. If this occurs, the likelihood of leakage increases, so please remove and dispose of these batteries.

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