A whippersnapper is a “diminutive, insignificant, or presumptuous person,” and, if we needed proof that it was not a compliment but a term of reproach, here is the word used in a lengthy harangue by Edgar Allan Poe, from his story “Loss of Breath”:
"Thou wretch! – thou vixen! – thou shrew!" said I to my wife on the morning after our wedding, "thou witch! – thou hag! – thou whipper-snapper! – thou sink of iniquity! – thou fiery-faced quintessence of all that is abominable! – thou – thou –"
The speaker in the story is then, gratifyingly, bereft of breath and stops.
Whippersnapper is usually used in a much milder way, as by an older person in order to emphasize the youth of the person being addressed. It seems to have come from an earlier word, snippersnapper, which was first used, with the same meaning, in the late 1500s. It may also have been influenced by whipster, a word used in much the same way by Shakespeare:
I am not valiant neither, but every puny whipster gets my sword.
Whippersnapper’s popularity peaked in the 1930s, making it seem to us, despite its Renaissance origins, recognizable and oldy-timey.