I was taught the same 1.5 diameters but have to admit to violating it all of the time within reason depending on the operation.
Drilling on the lathe. The concern with sticking too much material out is run out causes an imbalance which could cause the material to bend and start whipping. Lots of videos out there showing what happens when too much unsupported material sticks out of the back of the head stock.
Cutting on a lathe side loads the material being cut. So it really sets you up for buckling the material and getting it to whip. Parting is naturally a lot more side load than cutting. Bump knurlers too, that's why a lot of us swear by the scissors type.
Liability aside (long time since I had the classes in school), equations are:
deflection = (force x length) / (cross sectional area x Young's modulus).
Stress in a simply supported beam = (moment x distance from the neutral axis) / moment of inertia
Young's modulus for steel is around 30,000,000 psi. Moment of inertia for a beam with a rectangular section is = ( base x (height)^3 ) / 12. Yield strength varies depending on the alloy, but 30,000 psi would be a pretty safe number for mild steel. Moment is the force applied times the distance. Distance from the neutral axis is the edge you're touching relative to the center of the part.
Cutting to the quick, stress (force per unit area) is what buckles the steel. The material acts like a spring (elastic region) with a side load until you stress is above the yield strength, then it buckles (plastic region). Double the thickness and you increase its stiffness by a factor of eight. So you are "safer" hanging a 2" round 12" outside of the chuck than you would be with a 1/4" round 12" out.
I keep work really tight to the chuck when parting, go less than 1.5 diameters hanging out. Other than that, I'll play with the depth of cut and let the chips tell me if I'm at risk. Lots of chatter, be really careful. Nice curly Q's, pretty safe though naturally with each cut you're making the diameter smaller and increasing the risk of buckling.
Bruce