In some ways, that's true. Most of us cherish our freedoms, most of us hope to move about the world without meeting violence, hatred and terror.

But this was also a homophobic attack. Omar Mateen chose a gay nightclub as the theatre of his warfare. He had expressed disgust at gay affection. This was a hate crime - and we should say so.

There has been a peculiar resistance to call this atrocity homophobic. Some media reports omitted the fact that Pulse was a gay venue, as if this were not relevant. Mr Turnbull was initially reluctant to even mention the context of the attack. Only in his second public statement did he acknowledge it was "directed by a murderous hatred of gay people".

In Britain, gay Guardian columnist Owen Jones stormed off a television set after fellow panellists insisted Mateen had attacked "human beings" rather than specifically LGBTI people.

How does this become a point of contention? Whatever his sympathies or connections, Mateen had a choice of many targets that night. He chose to kill gays - that much seems clear.

In recognition of this fact, gay communities the world over are grieving. It is their safe space, the gay bar, that has been violated - a space made necessary by hundreds of years of persecution and hate. That is why it is the rainbow flag you will see bathed in candlelight at vigils this evening. That is why Sydney's Town Hall will be lit up in pink, and Canberra's Kings Avenue bridge covered in rainbow lights.

Words matter, and labels matter. The way we classify stuff is a window into our motives, our agendas, our prejudices. And so a white guy who massacres dozens in Norway becomes a madman, not a terrorist. And a jihadist who murders homosexuals hates freedom, not gays.

It's hard to understand why some observers want to deny LGBTI people this ownership. But what it says is macabre. It shows how badly they want every act of terror to fit into a narrative of us-versus-them, Islam versus the West, hatred versus freedom.

For mine, I don't see how Mateen's attack undermines that narrative at all. Gay liberation should be a freedom cherished and celebrated by all. Straight white Christians should be as hurt and angry about this atrocity as any subway bombing or school shooting. And yet it seems it Is difficult for some people to empathise unless the attack is generalised and nationalised, post hoc, into a broad-based act of capital-T Terrorism.

Politicians who are actually gay saw things in a slightly different light. Liberal MP Trent Zimmerman, a factional ally of the Prime Minister, readily agreed the attack was "an assault on all of us". But he also acknowledged it represented a new dimension in modern jihadism; the first time gay people had been targeted in the West.

There are precedents, of course. In 1999, a British neo-Nazi bombed the Admiral Duncan gay bar in London's Soho. And modern jihadists have targeted other groups such as the journalists of Charlie Hebdo and Jewish communities around the world.

"This has opened up a new front, in that it has broadened those specific attacks to include people based on their sexuality," said Zimmerman.

Dean Smith, a gay Liberal senator from Western Australia, described the Orlando atrocity as deliberate, calculated and "tremendously upsetting". And it had terrorised LGBTI people in every continent, he said, reminding them of hatred that was probably closer to the surface than most cared to admit.

"Debates about tolerance, debates about understanding [and] calls for empathy are not academic," Senator Smith said. "Calling out prejudice and fear and intolerance should be the first task of people in public office."

And he's right. There is nothing to gain in papering over Mateen's motivations and making the gay community invisible yet again. But there is everything to lose in refusing to accept this as a hate crime - one that hurts us all by targeting our most vulnerable.