I’m not sure how I managed to miss the fact that leadership of the Labour party is a hereditary position. Apparently, Labour hasn’t even got round to abolishing the rule of primogeniture, as the defence secretary, Michael Fallon, reminded us on BBC Radio 4’s Today programme on Thursday. Fallon suggested that Ed Miliband “stabbed his own brother in the back”, appearing to suggest that modern political parties operate a line of succession similar to the royals.

According to this hitherto unknown rule, David Miliband’s expectation that he would become Labour leader was no less solid than the Prince of Wales’s claim to the throne; Ed’s challenge was a constitutional outrage, a bit like the Duke of York suddenly announcing he’d like to have a go after his mum dies. The whole point of male primogeniture is that it’s an immovable thing, ensuring that the firstborn son smoothly assumes his rightful place when his turn comes round.

What’s that you say? The previous Labour leader, Gordon Brown, is neither dead nor father to either of the Miliband boys? Look, we’re talking about myths and archetypes here: think Cain and Abel, Jacob and Esau, Romulus and Remus. True, none of these individuals aspired to become leader of the Labour party, as far as I know, but obviously the same rules apply. Just ask the defence secretary. And, sadly, Fallon isn’t the only person who thinks like this.

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Later this month, the Duchess of Cambridge will give birth for the second time. Where are the crowds, waiting eagerly outside Buckingham Palace? Two years ago, the birth of Prince George was a massive event, at least as far as the media were concerned; in the days leading up to it, camera crews and correspondents set up a long line of stalls in The Mall. Whether the public was quite so fascinated is another matter, with just over half the population telling a polling company that they weren’t interestedin the birth. But TV and newspapers breathlessly anticipated an announcement that the third in line to the throne had finally arrived. Prince George can expect a pretty long wait, judging by his grandfather’s experience, but something about the idea of a firstborn clearly entranced the media.

Whatever happened to equality? I know it’s nonsense even to mention it in the same breath as the royal family, but we live in a country where equality is written into the law. There is no logical reason why the elder Miliband son should have had a clear run at the Labour leadership; the whole thing could just as easily be rephrased to ask why David stabbed his younger brother in the back.

To be clear, I don’t think that makes sense either, and I’m amazed that anyone should think in such Old Testament terms in the 21st century. It’s true that two members of the same family competing for the same position is likely to create tensions, but that’s a different matter. Someone might think twice about applying for the same job as a brother or cousin, but there’s no special responsibility on the younger member of the family to avoid conflict.

To think otherwise is pre-modern. Fraternal rivalry is linked to a cascade of patriarchal and offensive ideas about the family, such as placing a higher value on sons than daughters. The British monarchy has only recently ditched male primogeniture, a move rendered mostly academic by a line of firstborn sons, and I don’t think we should emulate the Windsors’ continuing attachment to hereditary positions. People who criticise Ed Miliband may not realise it but they’re unconsciously replicating tribal notions about family roles. In pre-modern families, the boundaries were set in stone, with dire effects on women, younger sons and anyone who tried to rebel.

Even Marine Le Pen, standard-bearer of the French far right, has ditched the notion that children should unquestioningly accept the authority of their parents. Her father, Jean-Marie Le Pen, founded the Front National and remains honorary president, but his offensive remarks about the Holocaust and France’s current prime minister, Manuel Valls, are more than she can stand.On Wednesday, she accused her father of adopting “a strategy somewhere between scorched earth and political suicide”, and announced she would block him from running as a candidate in regional elections. No doubt she is worried about his effect on her hopes of a presidential bid, but her stance breaks taboos which are normally regarded as sacred on the political right.

If a son had behaved in the same way, comparisons with Oedipus would have been inevitable. But it is when women enter the narrative that the patriarchal nature of traditional assumptions about power within families becomes apparent.

What if David Miliband had a younger sister? Would she have faced an expectation that she should abandon her political ambitions for the sake of her elder brother? In the modern world, that would rightly appear antiquated and sexist. And how does this unspoken rule apply to twins? If Angela and Maria Eagle both wanted to stand for the Labour leadership, would the one who was born second be expected to step aside? Does a gap of 20 minutes in birth order count as much as the four years that separate the Miliband brothers?

Family rivalry has produced compelling myths and great literature. So has the conflict between rival monarchs, dynasties and empires down the ages. But we no longer live in that pre-modern world, even if some Tories pretend not to have noticed. Whether we are talking about the Miliband brothers or anyone else, hereditary privilege has no place in modern political parties.