He said "Idiom continuity". That doesn't mean they all have to be opposites, he's just extending the metaphors in whatever direction he fancies.

Skeletons in your pantry: Your dark cooking experiments when you were drunk, high, or broke

Clearly it's a function of |y|.

One way's flammable

The other's inflammable

Remaining motionless at room temperature.

It's "go up in flames" right? So the opposite would be "not catch on fire?"

"going sideways" is also bad.

“Going forward in flames” is what it should be. You’re in flames, but you’re not going up, down, or sideways (all bad), but just going forward knowing the flames will probably subside.

If someone 'lets the cat out of the bag' they have shared secrets.

If you've got a whole bag it means you haven't let any out

Boo, let’s just steal it and cut his name out!

Oh, that's disappointing.

What it mean?

Opposite of throw in the towel.

Continuity is consistency across a spectrum.

I think it's continuity, like a spectrum. At one end is thin ice, the other is thick ice. etc