He sounds like he's being an arrogant twunt and it does sound as though he has issues with a) not being in a management role any more and b)being managed by women.
He's certainly lacking in emotional intelligence and if he's been any sort of a manager, he should have an understanding of that - but clearly he doesn't.
But those are his issues and he's the one who needs to adjust to the new situation, with your feedback and guidance.
Does the job spec say he should work effectively in a team? As he's clearly not doing that (by getting others' backs up), and as you can cite specific examples, you can feed this back to him on Tuesday as an area he needs to address.
But you should also praise him for what he is doing right - for instance, some of his comments may be valid and help you in the longer term - however, there is an appropriate way to feed that back and he needs to know what's appropriate and what's not.
I'd also suggest you keep your own manager informed about the issues because what you may find is that he will go behind your back to whinge about you to her - I've encountered this sort of behaviour from men who don't take kindly to a woman boss so it's as well to be prepared and firm with him.
And then best to document your feedback chat - perhaps in an email copied to your boss - so that if find he carries on underperforming you can get rid more easily - although presumably his probationary period would make that easier.
It's always difficult to do - but try to separate the behaviour from the person, especially when you talk to him.
Although he might have an irritating personality, it's his behaviour which needs to change iyswim. Good luck for Tuesday, let us know how it goes.