The Age explains this better than Mr. Heiner does; he “signed away” his (Australian) citizenship. He “signed away his citizenship when he filled in a form to take on post-nuptial Irish citizenship after marrying an Irish woman”.

After having a child with “another partner” on 2011 his application for citizenship for that child was rejected because Mr. Heiner is not an Australian citizen any longer because he signed the right away.

There is no ‘birthright’ citizenship in Australia, and at least one parent must be an Australian citizen for the child to become a citizen.

Given Australian government's slapdash attitude to citizenship for some really bad people, it's hard not to sympathise with Mr. Heiner, since his Australian roots go back a couple of centuries. But, he does have to take responsibility for his personal actions.