I don't think Australians hate Americans as individuals. I like nearly every American I have met. In person you are really friendly generous people. But when we think of you as a faceless group of people, you have some cultural quirks that rub us the wrong way. These are broad generalizations that don't apply to every American or every Australian but I think this is the starting point for where the problem is.

Americans have a culture where it is acceptable and even encouraged to "put yourself out there" and "sell yourself". This means that you will talk about your big promotion, who your parents are, how much money you make, how great you are at something.

Australians (and NZ / UK too I think) have a culture that is influenced by tall poppy syndrome. So we are very careful to never talk about ourselves. There is a social ettiquite where you play down your acheivements, then the other person asks for more detail, it's a verbal dance we do. Part of the dance is playing down your acheivements, but part of the dance is also the other person asking the right questions so that you eventually tell them the full story anyway. Both people have to play their part for it to work properly, we really do want to tell you how awesome we are but we have to wait for you to ask the right questions.

The problem is that Americans don't know how to do the dance at all. We play down our acheivements and the American wont ask the right questions so that we can tell them what really happened. Then immediately afterwards they will just tell me flat out all about how great they are without playing it down. It makes you seem self centred and arrogant because youa re acting the same way as a self centred arrogant Australian would do when they deliberately ignore the conversation ettiquite to talk about themself. The truth is that you aren't, you were just completely unaware that there was a whole conversation dance that you were supposed to do. The sad part is that sometimes when the American realises that things aren't going well, they try harder to be friends by talking more and more about how great they are which just makes things worse.