After the first round of the French presidential elections, several liberal commentators condemned the defeated leftist candidate Jean-Luc Mélenchon for refusing to endorse the centrist Emmanuel Macron. His decision was portrayed as a failure to oppose the far-right Front National, and it was argued that many of his supporters were likely to vote for Marine Le Pen in the second round. Comparisons were drawn with the US presidential elections and the alleged failure of Bernie Sanders supporters to back Hilary Clinton over Donald Trump.

Underlying these claims is a broader and increasingly popular notion that the far left and the far right have more in common than either would like to admit. This is known as the “horseshoe theory”, so called because rather than envisaging the political spectrum as a straight line from communism to fascism, it pictures the spectrum as a horseshoe in which the far left and far right have more in common with each other than they do with the political centre. The theory also underlies many of the attacks on the leader of the UK Labour Party, Jeremy Corbyn, who is accused of cosying up to authoritarian and theocratic regimes and fostering antisemitism within his party.

Taken one by one, these claims do not withstand scrutiny. Did Mélenchon give succour to Le Pen? No: he explicitly ruled out supporting Le Pen, and most of his supporters voted for Macron in the second round. Are there antisemites in the Labour Party? Yes: but there are antisemites in every British political party; the difference is that repeated incidents of racism in other parties go unremarked (as does Corbyn’s longstanding record of anti-racist activism).

Fans of the horseshoe theory like to lend their views weight and credibility by pointing to the alleged history of collusion between fascists and communists: the favoured example is the Nazi-Soviet Pact. But – aside from the fact that the Soviet Union played a vital role in defeating the Nazis – it is patently absurd to compare Stalin to present-day leftists like Mélenchon or Corbyn.

Can we instead find convergence between far left and far right at the level of policy? It is true that both attack neoliberal globalisation and its elites. But there is no agreement between far left and far right over who counts as the “elite”, why they are a problem, and how to respond to them. When the billionaire real-estate mogul Donald Trump decries global elites, for example, he is either simply giving his audience what he thinks they want to hear or he is indulging in antisemitic dog-whistling.

For the left, the problem with globalisation is that it has given free rein to capital and entrenched economic and political inequality. The solution is therefore to place constraints on capital and/or to allow people to have the same freedom of movement currently given to capital, goods, and services. They want an alternative globalisation. For the right, the problem with globalisation is that it has corroded supposedly traditional and homogeneous cultural and ethnic communities – their solution is therefore to reverse globalisation, protecting national capital and placing further restrictions on the movement of people.

Is there a more fundamental, ideological resonance between far left and far right? Again, only in the vaguest sense that both challenge the liberal-democratic status quo. But they do so for very different reasons and with very different aims. When fascists reject liberal individualism, it is in the name of a vision of national unity and ethnic purity rooted in a romanticised past; when communists and socialists do so, it is in the name of international solidarity and the redistribution of wealth.

Given the basic implausibility of the horseshoe theory, why do so many centrist commentators insist on perpetuating it? The likely answer is that it allows those in the centre to discredit the left while disavowing their own complicity with the far right. Historically, it has been “centrist” liberals – in Spain, Chile, Brazil, and in many other countries – who have helped the far right to power, usually because they would rather have had a fascist in power than a socialist.

Today’s fascists have also been facilitated by centrists – and not just, for example, those on the centre-right who have explicitly defended Le Pen. When centrists ape the Islamophobia and immigrant-bashing of the far right, many people begin to think that fascism is legitimate; when they pursue policies which exacerbate economic inequality and hollow out democracy, many begin to think that fascism looks desirable.

If liberals genuinely want to understand and confront the rise of the far right, then rather than smearing the left they should perhaps reflect on their own faults.