Peter Hume: "What is "neoliberalism", pray?"

Well Peter, you set me a difficult task; do I explain the word in the nominal pejorative sense I tend to couch it in (which you ought to know so well by now), or do I elaborate?
We can surely dispense with the "neo", except to say it indicates the period of socialist or welfare-capitalism--the prevailing tendency postwar until its gradual erosion from the early eighties on. Less than 50 years then between classical and neoclassical political economy.
You will of course immediately object that we've never had true free markets, nevertheless I didn't invent these terms and they don't indicate anything untinctured, but rather prevailing tendencies towards privatisation, towards capitalism in a word, or if you prefer the standard euphemisms, the "free market", "free enterprise", "market society" etc, etc.
Of course neoliberalism also boasts a pseudo-philosophy of individualism, famously espoused by Margaret Thatcher; that there is no such thing as society, only individuals and families. Neoliberalism transcends such quaint homilies and neoliberal families today also pay homage to corporations.
There are differences in usage (of liberalism), say between Britain and the US, but the core values are the same and tantamount to social anarchy, or again at least nominally.
Ostensibly, true liberalism is akin to pre-Hobbesian survival of the fittest, a spurious kind of pseudo-Nietzschean realm of green-blooded individualism (bloody Romulens!).
In reality it's a craven form of materialistic opportunism that, if successful, goes on to employ all and any means to secure its ill-gotten stash.
Neoliberalism in the modern world is non sequitur since it makes its fortune from the commodified masses it despises, of whom it is of course a greasy member: narcissistic. Moreover it secures its wealth via social judiciaries, standing armies, the church (it's nothing if not pious) and other social securities it parasitises while feigning to despise them.
(Neo)liberalism has also had the dubious distinction to have presided over the two greatest financial crises in history, the Great Slump and the GFC.
They remain supercilious and uncontrite..

Apart from these small matters, "it's all good" as they say.

Looks like a string of mispresentation and abuse to me.

Which part is the actual definition that the supposed neoliberals actually agree with?

On the contrary, Peter. This is a fair assessment of liberalism. What part do you disagree with?

Why is it so hard for some to understand that Tim Flannery's approach is not unique or crazy? It doesn't refer only to climate change, nor to any particular topic. A global consciousness includes everything. Millions of sane and influential people on this planet understand that we are all one, that everything around us, our whole galaxy and its contents, originated in star stuff from one of an infinite number of big bangs. It makes no sense to fight against ourselves or those who try to lead us out of harm's way. That's the equivalent of drinking poison, smoking or taking drugs, and killing the nurses and doctors. Our only hope of peaceful, healthy, coexistence in balance with nature, which is us too (our very breath is water) is to live the principle of sharing and caring and overcome our fear of difference that prompts the need to dominate. It seems it will be a long time to the tipping point, but we may be surprised how close it is if we each do the little we can as long as we can, holding up our candles in the night, "you in your small corner, and I in mine".

I agree with your sentiments, Polly Flinders--fine words. But the reality is the world is divided as never before between rich and poor and Flannery is on record as supporting the "competitive" way in which the human world is currently arranged, notwithstanding that the game is insuperably stacked against the impoverished at home and especially abroad. Until Flannery says something to make me feel otherwise, I see him as just another instrumental stooge of the state. Instrumental reason has no conscience.