Thanks for the responses.
Let me amplify on the health angle, since I may have been to cryptic in my reference.
My limited understanding of the theory of Qi movement in the body is that all flows are not equal. For instance, the Microcosmic Orbit seems always to be discussed as if it should go in only one direction. Since the heart, liver, intestines, and other organs are not symmetrically positioned in the body, one could argue that certain exercises promote proper circulation in one direction; whereas others would alter the proper direction of the flow. I think the criticism of left-side forms proceeds from this kind of view.
One of many difficulties I have with this sort of theorizing is that some people also purport to make allowances between men and women, arguing that some Qi Gong exercises should proceed in one direction for men and in another for women. Presumable this difference is supposed to reflect Yin/Yang differences.
Another argument I can think of for one-sided form is that some argue that efficient martial training should not be 100% bilateral. For instance, many argue that training weapons equally in both hands simply decreases the amount of training available for the dominant hand and dominant side. Someone who has spent half his or her time training a sword in the right and left hands will, at any one time, be able to display only half the skill of someone who has trained exclusively with one hand. One counter argument is that training with only one hand is putting all one's eggs in one basket.
Similar thinking in favor of one-sided training holds that the techniques one should use against "lefties" should not necessarily be mirror images of the techniques one would use against "righties." Consider, for instance, how professional boxers train and fight or how baseball players pitch and bat against left- and right-handed opponents.
I would guess that weapons theory and training need not be the same as bare hand; nevertheless, I can see something to the argument that it is better to specialize the dominant hand for some things.
One last comment I would like to make is that, unlike in the case of the form, every push hands drill I have every learned seems always to have had right and left variants, implying that bilateral barehands training should be the norm. The only sense I have been able to make of all this is that the form may be dedicated to teaching principles and that partner training may be the appropriate arena for actual training of applications.