It is not really possible to know how people come to identify themselves very strongly with their home country. It is not possible to say with certainty why some people become very patriotic and would do things like wearing the flag as a cape while others would prefer not to engage in such activities. It seems to come down to a set of individualized factors.
We know that people generally want to feel special and unique. At the same time, we know that people want to feel like they belong to a group and are accepted. Different people find different ways to express their uniqueness while still feeling like they belong. With some people, showing patriotism can be a way of announcing their group identity in a way that makes them feel that they belong. They then try to express their individuality in different ways.
However, it is really not possible to know why a person chooses to express patriotism. It could be that the person has entered into a stage that psychologists call “identity foreclosure.” That person might have decided to identify with Australia as a way of conforming and of making a commitment to an identity (that of an Australian) without having to decide who they really are. These people have become patriotic in a mindless way that is based on a desire to conform. On the other hand, the person might have reached the level of “identity achievement.” They might have actually thought carefully about how they want to present themselves and might have decided that they want to be patriotic. They might have decided that they identify strongly with Australian values.
We cannot know what has impelled any individual to become patriotic in a demonstrative way. The decision could have been made through a lot of thought or it could have simply been made in a mindless, conformist way.