Father Brennan's departure means the heart of the Jesuit community in Canberra, Xavier House in Yarralumla, will close and the property put on the market.

Father Brennan, 65, will finish his role as chief executive officer of Catholic Social Services Australia in Canberra to become rector of Newman College at the University of Melbourne.

"The Jesuit order, we've had a presence in Canberra for the last 51 years but sadly the time has come. I'm the last one to leave," he said.

Giving a wide-ranging farewell speech at the Australian Centre for Christianity and Culture in Barton on Wednesday night, Father Brennan expressed his fears for the future of the Catholic Church unless it engaged in more open dialogue on issues such as women priests.

"I've long been a supporter of the idea of women being priests," he said.

"We live in a society where I look at my own family history, my own mother was one of the first women doctors at the Mater Hospital in Brisbane, my four sisters are all competent professionals and my nieces not only imagine but they've known a woman prime minister, a woman governor-general, a woman chief justice.

"So the need for the Church to adapt and ensure equality for everyone, I think, is essential."

At Wednesday's forum for Concerned Catholics of Canberra Goulburn, Father Brennan referred to Pope Francis' view that a church that lost its humility and stopped listening to others "loses her youth and turns into a museum".

Yet that thinking did not extend to speaking about women priests.

"The official position is no longer comprehensible to most people of good will, and not even those at the very top of the hierarchy have a willingness or capacity to explain it," Father Brennan said.

Father Brennan has lived in Canberra permanently for 11 years but been a fixture on the political scene for nearly 20 years, prominent in Aboriginal reconciliation and native title debates.

"Over the last 30 years or so, I've had good access to Parliament House, good access to the press gallery. I'll miss some of that but I'll be turning 66 next year and the opportunity to [be] living life with 250 students at the University of Melbourne who might be a bit wondering about the world and what the Catholic faith is about, was too good to resist," he said.

He chaired the National Human Rights Consultation Committee established by the Rudd Government in 2008.

And most recently, he sat on the expert panel for the religious freedom review set up in 2017 by then prime minister Malcolm Turnbull.

Father Brennan said the recommendations to come from the review never went anywhere, because some appeased the conservative arm of the Liberal Party and others the more progressive members.

But he believed that would change and the Morrison government would enact a "responsible" Religious Discrimination Act.

Father Brennan maintained the fiasco around sacked rugby player Israel Folau was not a case of religious freedom.

"I have studiously avoided the issue because I don't think it has anything to do with freedom of religion, I think it's all to do with freedom of contract and I've been somewhat amused by the number of people who have pontificated about the issue," he said.

"Suffice to say, he and Rugby Australia have the best lawyers in Australia. They were locked in a room for three days behind closed doors and they couldn't reach a breakthrough, which tells me as a lawyer, it must be a very vague contract. So it's an issue about what's in his contract, not about freedom of religion."

Father Brennan was also awaiting the outcome of Cardinal George Pell's appeal against his sexual abuse conviction, saying the priest was either "a paedophile or the biggest scapegoat the country has known".

"Perhaps Cardinal Pell is a paedophile who has effectively groomed the Church as an institution all the way to the top. But then again, perhaps he is not a paedophile and it has reached the stage in Australia that 12 of his fellow citizens were prepared to convict him of offences beyond reasonable doubt despite all manner of improbabilities because they don't trust him or our Church, no matter what we say or do," Father Brennan said.

He added: "I believe in two systems - I believe in the Catholic Church and I believe in the Australian legal system. And let's hope the legal system gets it right".

Father Brennan said he would be leaving Canberra later this year and the Jesuits would be selling their property on Empire Circuit, Yarralumla.

"I think it'll go on the market sooner rather than later and given it's in the heart of the embassy belt, 200 metres from the US embassy, I would think some of the embassies might be interested in it," he said.