Challenging Privilege

I have a good male friend who, in many ways, has been moving along the path towards being a good feminist/pro-feminist ally.
However, every now and again I still catch him saying something that screams of privilege, such as “do you really think women are oppressed in Australian society?” (To which I replied, that although it’s not as extreme as in a country like Iran, there are a multitude of lesser oppressions that Australian women have to cope with.)
Or “men and women will never be completely equal because men will always be physically stronger and better able to do things like open jars etc” Get real!
He calls himself a feminist and is interested in being active in the feminist movement, which is a great thing.
I think his problem is that he still feels feminism to be ‘against’ men to some degree, which leads him to be against women-only spaces.
Does anyone have any strategies to help others recognise their privilege? I hear of lots of male feminists who have ‘click’ moments, any advice on how to help my friend reach his?