Apart from the fact that Mr. Avery quite incidentally got the weather correct, the real irony is that both Mr. Avery and Scout did not know anything about the Rosetta Stone. Here is Scout's take on Mr. Avery.
For reasons unfathomable to the most experienced prophets in Maycomb County, autumn turned to winter that year. We had two weeks of the coldest weather since 1885, Atticus said. Mr. Avery said it was written on the Rosetta Stone that when children disobeyed their parents, smoked cigarettes and made war on each other, the seasons would change.
The Rosetta Stone is a text written in three languages (hieroglyphic, demotic, and Greek) by a group of priests in Egypt to honor the Egyptian pharaoh. It lists the achievements of the pharaoh.
The irony is that Mr. Avery can use something scholarly to persuade children that he can preternaturally predict the weather and the behavior of children, when he does not understand something himself.
The other irony is that in honor of Mr. Avery (or to mock him), Jem and Scout make a snowman. Atticus eventually yells at the children for mocking a neighbor.
In Chapter 8 of Harper Lee's novel, To Kill a Mockingbird, Mr. Avery's declaration concerning the season's changing when children were bad came true, much to the chagrin of Jem and Scout.
Mr. Avery said that it was written on the Rosetta Stone that when children disobeyed their parents, smoked cigarettes and made war on each other, the seasons would change.
Shortly after, Scout awoke to a sight she had never seen: Snow. Mr. Avery's prediction had come true, and Jem and Scout felt that it was partly their fault. Later, Mr. Avery made another affirmation:
"See what you've done," he said. "Hasn't snowed in Maycomb since Appomattox. It's bad children like you makes the seasons change."
Scout responds that
"... I did not wonder where Mr. Avery gathered his meteorological statistics: they came straight from the Rosetta Stone."
Since Mr. Avery had twice predicted correctly, Scout was sure that he had again gotten his information from the Rosetta Stone. She obviously did not know the true origins of the stone, one of history's first forms of written communication.