Well, I'm WAY behind now. Have some catching up to do this evening.
Uh... yeah... I'm guessing you're just joking around, but in case you aren't aware of that sabre dance...
Unless I'm misremembering, your dad would be referring to a whole different kind of sabre dance, involving a tremendous amount of metal, orders of magnitude more energy, and ended up 9 out of 10 times killing the "dance partner." I could only find (in a quick youtube search) one instance on video. But in actuality, it happened quite a few times. It was a notorious danger in coming in for a landing in the F-100 Super Sabre. If I recall the mechanism correctly, if you got "behind the jet," you could end up allowing the Angle of Attack of the air over the wings to get too high (angle that the air hits the leading edge of the wings; think of the air hitting the bottom of the front of the wing as "high angle of attack," the air hitting right at the front edge of the wing as "low angle of attack.") This high AOA eventually causes causes more drag than lift, and the jet slows and starts dropping out of the sky. So you increase power, but you can't let the nose drop or you will pancake. But the increase power can't overcome the drag caused by the high AOA, and you keep slowing down. You're still trying not to pancake, so you try harder to climb. Which increases the angle of attack more. Eventually you get to a stalemate, but it is an unstable stalemate. If you pull the control stick further back to climb higher (which the pilot in this video apparently did), you go beyond a critical angle of attack where the wings stall (or one does first, in this case). If both stall at the same time (not the usual case), you're going to pancake anyway. You can see in the video what happens if one wing stalls before the other.
I only ever heard of it happening with the F-100 Super Sabre.
I first saw this footage--or very similar footage--in 1961 or '62, when my Dad took me to see the feature film X-15. It was on a double feature with Voyage to the Bottom of the Sea, and it was at the old Colonial Theater in our hometown. As you might infer, it left quite an impression on me.
As David Letterman used to say, "You're not dealing with a chimp, here, my friend."
Just to get back on-topic:
I might have spoken prematurely when I named the girl in pink "Katie Sunshine of the Sabre." Check out this young lady, who reminds me a bit of Catherine O'Hara back in her SCTV days: