The phrase "don't be that way" is a line from the Benny Goodman jazz standard with the opening line "April skies are in your eyes." In this context, "don't be that way" is an expression urging someone not to act a certain way or exhibit a certain behavior.
Note: The provided meaning of the answer is for the latest New York Times crossword puzzle clue: Benny Goodman jazz standard with the opening line "April skies are in your eyes". Explanations are generated by AI and may be inaccurate.