*grabs her spinning head*
As far as I can tell, your "symmetry" refers to who's allowed to do what, and requires that each person be allowed to do the same things.
It seems to get sticky when you talk about needs. People like to use the phrase "I need you to -----" because it sounds like an "I" statement. But really it's a "you" statement, a nice-sounding way of saying "You need to -----"
It's fair to have your own needs, i.e. what you require independently as an individual, in and of yourself ("I need to -----"). I don't believe it's equally fair to have needs "on behalf" of another person ("You need to -----").
So it's fair to say "I need to only be in relationships where I'm the primary partner." But it's not fair to say "Because I need to be the primary partner, you're only allowed to date other women on Tuesday nights under a half-moon on even days of the month."
You have the right to communicate what your personal needs are, whether or not your needs are being met, engage your partner in finding a compromise so that both your needs can be met, and to leave that relationship if a solution cannot be found. I don't feel that you have the right to dictate your partner's behaviour under the guise of "meeting your needs." Bottom-line, it's your own responsibility to meet your needs, not your partner's.
“As I am sure any cat owner will be able to tell you,
someone else putting you in a box is entirely different
from getting into a box yourself.” —bisexualbaker