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Both "don't teach your grandmother to suck eggs" and "teach your grandmother to suck eggs" are in common use, with the longer form meant to dissuade the listener from trying to instruct the speaker on some activity in which the speaker is more accomplished. The shorter form is meant to advise the listener that his intended instruction to a third party is, likewise, unnecessary. Both forms originate in a time when false teeth were less common than they are now, and raw or soft-boiled eggs were a preferred form of nourishment for many older people.

A little something extra:

Teach your grandmother to suck eggs. Attempting to teach your elders and superiors. The French say, “The goslings want to drive the geese to pasture” (Les oisons veulent mener les ois paitre).

from Dictionary of Phrase and Fable; 1898; E. Cobham Brewer (1810–1897)