Why does fluid the backward curl as it gushes out from the nozzel in the forward direction?

That sort of phenomenon is called a Kelvin-Helmholtz instability and it arises when you have a gradient in velocity perpendicular to the bulk flow (also called shear).

In this case, you have a jet coming out with some velocity into an ambient gas with some other velocity (possibly even zero velocity). Right outside the nozzle there will be a very big jump in velocity across the interface between jet and not-jet. Viscous forces will work to slow down the jet along that interface, while they will also speed up the non-jet gas along the interface. These roll up into vortices.

These vortices may be nice and clear, or they may be very tiny and then get all jumbled up due to turbulence. It depends on how strong that gradient is and how viscous the fluid is. But that's a whole field on its own, so its better to ask questions specific to that if you are interested!

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That figure looks like it's from a subcritical liquid jet injecting into a gas. In that case, the mechanisms are similar to what I described above, but now you have surface waves along the liquid. Those surface waves will lead to a complex set of break up mechanisms depending on the ratio of viscous forces and surface tension forces (known as the Weber number). It looks like there's some atomization and stripping of very small droplets, which get pulled around in those Kelvin-Helmholtz structures (or the turbulent structured those turn into), which is why it looks kind of misty around the coherent core downstream.