Beware common sense, I say. Those who cheer it on are inevitably dull enforcers of the status quo. Witness the headlines around Sara Thornton’s comments to the annual National Police Chiefs Council about the police not having the time or resources to investigate misogynist abuse.

She understands why treating misogyny as a hate crime may be desirable. “But we do not have the resources to do everything that is desirable and deserving … I want us to solve more burglaries and bear down on violence before we make more records of incidents that are not crimes.” And a chorus of the usual suspects joins in, of course: what we want are old-fashioned police on the streets solving proper crimes. Who doesn’t want that? Only, apparently, members of “the PC brigade” – a somewhat shadowy organisation formed decades ago. We operate almost as freemasons with our weird attitudes about not wanting to be hated and abused on the basis of our gender, ethnicity or disability.

Thus common sense is pitted against out-of-control political correctness as though I have the simple ultimatum of having my burglary solved or reporting wolf-whistling to the police. The terms in which this is all debated are antediluvian.

For the record, I have never had a burglary solved, nor ever really expected to. I have had very PC policemen sit in my living room telling me that they understand how being burgled makes a person feel violated, as they too have been violated. But any suggestion of catching the bastard? Never.

So yes, I would like the police to sort out this stuff. Just as I would like the horrific knifing around the city to be stopped. If this is the core policing work that Thornton wants doing, we can all agree on this. This requires more resources, and the party of law and order has systematically cut police numbers.

In the justice system, it really is not a case of women and children first, but last

Crimes of violence frighten all of us, but this throwing out of misogynistic abuse and historical child abuse as issues that unjustifiably take up valuable police time is not the way forward. Common sense, I am afraid, does not recognise that policing has changed because society has changed. Nor does it make the links between different types of crimes.

Wolf-whistling does indeed sound harmless, but what women are really complaining about is street harassment with an implied threat of violence. Is this a crime or merely anti-social behaviour? If the police won’t take it seriously, who will?

Domestic abuse used to be seen as a private and trivial issue, but we now see it differently. Two women a week are murdered by their intimate partners. There is domestic violence in the background of many of those who go on to terrorise others.

The real issue is that evidence-gathering in a digital age is a hugely time-consuming business. This is partly why we currently have the lowest convictions for rape for a decade, as victims’ texts are used as evidence of supposed consent. The Crown Prosecution Service is in a state of chaos and the relationship between the police and the CPS is part of the problem. The police are also having to deal with the effects of austerity, operating as the frontline of social services, often dealing with homeless and mentally ill people. None of this is crime-solving, but where else are people to go?

An over-stretched service cannot deal with this new hate crime of misogyny, although no one is suggesting that attacks based on race, religion or disability should be decriminalised, are they? What is being said then, is that crimes against property are more important than crimes against women, which is how the law has operated for a long time. Common sense tells us this is just the way it is. If every case of child abuse were brought to court, there would be no time for anything else. In the justice system, it really is not a case of women and children first, but last.

When it comes down to priorities, I would rather the police investigate a man threatening my daughter on the bus than whether a car has been scratched. Thornton said: “It is this core policing which is seriously stretched. This is surely part of the police covenant with the public.”

Half the public are women. I know I am deranged with political correctness to say this. But where are we in this covenant?

• Suzanne Moore is a Guardian columnist