"I do think it's important, actually, for those of us in uniform to be open-minded and be widely read," said Milley.
"I personally find it offensive that we are accusing the United States military, our general officers, our commissioned, non-commissioned officers of being quote 'woke' because we're studying some theories that are out there," he added, to which Gaetz shook his head in disagreement.
Critical race theory, a framework of ideas developed by academics of color for understanding the history of systemic racism, has become a flashpoint for the far right.
Former Republican President Donald Trump put the spotlight on critical race theory in September when he issued an executive order directing all federal agencies to cease diversity training among employees, just months after the country experienced nationwide protests against racism and policing following the murder of George Floyd.
In response to Gaetz, who is a staunch Trump ally, Austin said the Defense Department does not "teach" or "embrace" the theory, adding that he thought the congressman's line of questioning was "spurious."