I think what he's driving at is that your point relies on the assumption that neoliberalism is left wing, when this is not true.
I didn't say that all neoliberals were left wing.
I said that there were some people on the the left that were neoliberals.
Please understand this difference.
https://en.wikipedia.org/wiki/Neoliberalism#United_States
> Early roots of neoliberalism were laid in the 1970s during the Carter administration, with deregulation of the trucking, banking and airline industries,[144][145][146] as well as the appointment of Paul Volcker to chairman of the Federal Reserve.[21]:5
> During the 1990s, the Clinton administration also embraced neoliberalism[130] by supporting the passage of the North American Free Trade Agreement (NAFTA), continuing the deregulation of the financial sector through passage of the Commodity Futures Modernization Act and the repeal of the Glass–Steagall Act and implementing cuts to the welfare state through passage of the Personal Responsibility and Work Opportunity Act.[147][149][150]
You seem to presuppose your claims are de-facto correct; I don't think that is true.
"No true Scotsman"
See the 1999 Seattle WTO protests as an example of the left opposing neoliberalism.
Just because those that were further-left than centrist democrats existed and opposed their centrist democrats policies doesn't mean centrist democrats weren't considered "on the left" by a great many people, who would also be considered left of the Republicans at the time.