South African Arthur, who was fired on the eve of the 2013 Ashes after a run of defeats and replaced by national coach Darren Lehmann, will be plotting Pakistan's strategy for the three-Test series starting at the Gabba on Thursday.
Arthur, 48, said there was a part of him that still had a point to prove to his former employers. "I wouldn't be honest if I said otherwise," he told reporters.
"That's what happens. It's a ruthless world out there.
"I always maintain that I loved the first year and a bit of it. It was outstanding and I felt we made some significant progress.
"This series isn't about me against Australia. It's about two very good cricket teams going head to head. I hope that can be the focus."
Arthur said he was coming to terms with facing his former team.
"It's pretty surreal to be walking into the Gabba, coming back as a visiting coach," he said.
Arthur's tenure was marked by the so-called "homeworkgate", when four players - Shane Watson, James Pattinson, Mitchell Johnson and Usman Khawaja - were banned for one Test for failing to complete a written task set during a disastrous tour of India in 2013.
Australia pace spearhead Mitchell Starc has said the home team is "a lot closer" since Lehmann replaced Arthur.
"The team wasn't very close in those times but that's because of different characters," Arthur said.
"Since then the guys have matured and gone on ... Mitchell Starc is a world-class cricketer."
Arthur said he was prepared with some insider information about the current Australian players, but it was up to his Pakistan team to put it to good use.
"The intelligence is good. We'll be providing a whole lot of information," the Pakistan coach said.
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