There's a reason for the statement that "odd terms don't matter", but obviously it depends on the contest.
Suppose you are measuring a voltage from DC to 1Hz, and you know that you have a 50Hz interference from the supply line.
If the system if linear it is enough to low-pass filter.
The same if the system is not linear but with only odd order terms.
But the even terms are going to "rectify" your signal (in a sense), disrupting the DC accuray no matter how well you filter.
From another point of view - consider the frequency domain.
A second order term (x*x) becomes a convolution in the frequency domain.
If you make the auto-convolution of the 50Hz signal you get two peaks: one at 0Hz and the other at 100Hz.
The 0Hz peak is the one causing problems.
A third order term is a double-convolution --> peaks at 50Hz and 150Hz --> no problem at DC.