Imagine an Athenian who went on an overseas trip for a couple of weeks and returned to the city on 28 September. The traveller left before Pavlos Fyssas's assassination, and the awakening of media and government to the neo-Nazi threat, leading to the arrest of Golden Dawn leader Nikolaos Michaloliakos and some of its MPs and supporters.

The initial reaction of the traveller to the crackdown would be jubilation mixed with surprise: the change in the authorities' attitude following Fyssas's murder was dramatic. And yet, the same authorities have had detailed information about the party's criminal activities for years. Racist violence is experienced daily and has been widely reported by international media, national and international NGOs and the EU commissioner for human rights. Indeed, racist violence had become normalised for many. Legal and political authorities were unwilling to take action; Greece's anti-racist law was never applied (an improved version was recently rejected in parliament); and perpetrators of racist attacks were offered impunity.

Less than a year ago, Nikos Dendias, the minister of public order, insisted that no link existed between the police and Golden Dawn, and threatened the Guardian with a libel suit when it reported that policemen tortured anti-fascists. Yet in the wake of Fyssas's assassination, Dendias was forced to launch an inquiry into such links. Several senior officers were sacked or suspended. A day after the assassination, 32 legal cases were filed against Golden Dawn including violent, even lethal incidents.

Our Athenian would be puzzled by the obvious questions: why did the authorities not step in earlier? Why are they stepping in now? Could it be because a Greek has been murdered?

Golden Dawn should have been designated a criminal gang and legally confronted a long time ago. This course of action would have been automatic in most European countries. After the murder, European politicians indicated their displeasure, with several suggesting that unless Greece confronts the neo-Nazis it should not assume the EU's rotating presidency in January.

But perhaps the main motive in the government's fluctuating response has been political calculation: until very recently senior rightwing politicians and commentators suggested that the rightwing New Democracy (ND) party should consider entering a coalition government with the neo-Nazis, if they became more "moderate". The government presented the left and anti-fascist movement as one of the two pro-violence "extremes", even though they resisted Nazism all those years.

This historically ignorant and morally perverse "theory of two extremes" was meant to instil fear and turn people away from the leftist organisations and grassroots movements resisting neo-Nazi attacks and supporting their victims. The ND/Pasok coalition government now hopes that the exposure of Golden Dawn criminality will attract its voters to their natural home.

And so, the feeling is bittersweet: even if delayed, the heavily publicised arrest of the Golden Dawn leadership will be a relief to many. To the city's migrants, who may find it easier to walk the Athenian streets, to homosexuals, leftists, to all anti-fascists to everyone resenting Golden Dawn's shameless entry into everyday life and in the country's politics.

Every dark-skinned person had to take precautions in Athens. Evil walked the streets.

Little has changed at the institutional level, however. The application of the criminal law to thugs will not change the widespread racism fuelled by the New Democracy-Pasok coalition government. It was Andreas Loverdos, a prominent Pasok member at the time, who likened Golden Dawn to a "Greek Hezbollah" because they are "active in the big issues" and "create trust".

It was Vyron Polydoras, a former New Democracy minister, who urged a coalition with them. And it was prime minister Samaras himself who declared, in March 2012: "Our cities have been occupied by illegal migrants; we will take them back." Sticking to its word, this government launched the ironically named hospitable Xenios Zeus operation, rounding up dark-skinned people and detaining undocumented immigrants in camps euphemistically named "holding centres".

The same government repealed the reform of the 2010 Greek citizenship law, the first to offer second-generation migrants a potential entitlement to citizenship. The government and authorities criminalised HIV patients and drug addicts; persecuted and illegally detained anarchists and anti-fascists; slashed salaries and pensions; saw youth unemployment rocket to over 60%; shut down hospitals; and pushed universities to the point of collapse. This is the great paradox of dismantling Golden Dawn: the same government which threatens democracy and indulges fascism gives itself democratic credentials for its supposed curbing of extremism.

Golden Dawn is both a political party and a gang – and outlawing political parties often proves problematic and ineffective. The law can prohibit, but it cannot eliminate, fascist ideas; these must be confronted politically instead. For ordinary people, the struggle against Golden Dawn is not limited to the welcome though theatrical arrest of its leadership. Anti-fascism is a political struggle about the kind of life we want to live. It is fought daily by citizens, activists, civil society groups and migrant communities. It is a battle for democracy, solidarity and social justice. It cannot be won unless the systemic injustice of austerity is defeated.