I think most of Andrew's dislike of Ann comes from ego - or bruised ego.
As in the Apprentice, Andrew is quite full of himself.
He can pull straight men and gay men.
He's the sort of lad who thinks he could turn gay women straight.
And he probably finds his attitude works a lot of the time.
Usually, he's able to wrap old biddies round his little finger but it ain't working with Ann and he doesn't like it.
Ann's issues also come from ego.
She believes in an Ayn Rand type of world with heroic men and subservient women.
Fantasing herself to always be the heroine to the most heroic of men, she fundamentally can't accept other women as anything other than her inferior - and obviously the inferior of all men.
Blend Ayn Rand Objectivism with Roman Catholicism and you have a recipe for full-on Narcissistic Personality Disorder.
It ain't pretty - and there's never any shortage of everyday narcissism in the CBB house anyway.
It was a bit rich of Ann (and the others) advising Jess not to care what other people thought of her.
It certainly might do Ann some good to think a little bit about what other people think of her and perhaps consider moderating her behaviour accordingly.
Which is only what she wants Ashley to do and what everybody wants Dapper to do. Think about others and try not to hurt or offend them.