In a dramatic precursor to State of Origin II, Slater questioned former NSW forward Woods's right to have a voice in the media after copping heat from him last week.
The under-pressure Maroons coach also played down the spotlight on his own job, as Queensland fight to stay in the series at Optus Stadium in Perth on Wednesday night.
But Slater saved the most poignant response to a question around Woods's comments.
Woods made headlines last week when he labelled Slater a grub on Sydney radio, pointing to the fact he kicked then Wests Tigers prop John Skandalis in a game in 2006.
Asked about the issue on Tuesday, Slater questioned reporters if they really wanted him to answer before unleashing on Woods with a rally-like speech.
"When you hold a position in the media or in our game, I feel that's a privilege. And with that privilege comes a responsibility," Slater said.
"I sit in that position most weeks and you amplify your voice to millions of people. You're not talking to your mates in the pub.
"I know Aaron Woods. I actually ran into him three or four weeks ago at a footy game and he didn't voice that opinion then. He actually brought his son over to introduce him to me.
"When you degrade someone personally in a derogatory manner, you probably don't deserve one of those privileged positions that we're all in."
Slater was then interrupted by an applause from the crowd at Perth's public press conference, before telling them "I'm not done yet".
"You don't know what people are going through," he continued.
"And although I might be able to handle it, the next person mightn't be. Maybe our last coach didn't.
"I believe the character of a person is judged more on what they say about people and how they treat people, than what an individual says to create attention."
Green took his own life in 2022, one year after coaching the Maroons in the 2021 series.
A post-mortem found the North Queensland premiership-winning coach had been living with a "severe" and undiagnosed case of Chronic Traumatic Encephalopathy.
Tuesday's press conference was expected to centre around Slater's fight to keep the Maroons in the series and avoid a second straight defeat to NSW after last year's capitulation.
Slater has made a number of bold calls ahead of Wednesday night, headlined by the axing of captain Daly Cherry-Evans and Tom Dearden's move to the No.7 jersey.
Before a question was even asked by the press at Tuesday's press conference, a member of the crowd yelled out "you're under pressure Billy".
"What is pressure? To me, the opposite of pressure is comfort," Slater said.
"So you're either comfortable or you're in a pressure situation. And I think you earn that opportunity, whether it's a player or a coach.
"To be in this environment, you've earned that pressure. Because it means so much to the people of our states, it means so much to the people involved in the game.
"But of course there's pressure. There was pressure in grand finals. There was pressure in state of origin games and there still is.
"And the day there's no pressure, I'll be a bit worried."
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