No even-order harmonics in alkali gases? (Intuition for “symmetry in time domain'')

The polarizability can be expanded in the from:

In Alkali gases, it is said that $chi^3$ can be nonzero, and the combination of multiple waves can produce four-wave-mixing.

But what about $chi^2$?
I’ve heard it said that even order harmonics typically don’t occur in gases because of "symmetries in the time domain," as said here.

What does this mean exactly? To try to articulate my interpretation of this:

Am I understanding correctly that the statement is that processes like this are forbidden? If that interpetation is correct, why is that the case?