Don’t throw the baby out with the bath water

In achieving your aim (of pouring away the bath water), make sure you don’t do something else (pouring away the baby) that more than cancels out your achievement.

A certain Mr. Williamson, who had lived for years in London, decided to break with the past and seek a new life overseas. The day before he was due to sail he destroyed a pile of old correspondence, only to discover when it was to late that he had burnt his passport as well.

We can say of the careless Mr. Williamson that he had emptied the baby out with the bath water.

Another meaning of the prover is to reject all of something, including the good, because part of it is bad.