For me, primary and secondary labels are merely a way to describe the impact of relationships. Some people may contribute emotionally and physically to a relationship and others may contribute emotionally/physically/financially/parentally/every day chore-ly. To think that one will not have a greater impact than the other is naive. Therefore, I have no problem identifying one as primary and one as secondary. I identify as secondary in this way and am secure enough to recognize why, and the limits of my contribution. I have less impact across a broader spectrum of actually day-to-day functioning.
Love and connection are extremely important in a deep relationship, but it takes a lot more than those to raise children and run a home. If people are dedicated to performing the day-to-day functions of life as a team, no matter how many are involved, than that is the primary structure, in my opinion. Those that contribute on fewer levels will not impact the overall structure as severely and therefore are secondary.
Contribution = commitment
Commitment = impact
Impact = importance
Importance determines primary or secondary
Here's a quick exercise-- imagine what would happen if you removed each of your relationships from your life one at a time.
Which one would affect your life and the life of those around you most? Which one would cause you the most stress across a broad spectrum? Which one might cause you to lose your house? Which one might disrupt the lives of your family members? Which one might make maintaining your property a greater burden? Would one would cause your children distress, if you have them?
Emotional impact is one thing, but it is hardly the only thing. That is how I see the determination of primary and secondary relationships.