I don't think you're arguing against what the parent actually said. If you need your partner in order to be happy, and when they are not around you're unhappy, that is not healthy. Not healthy for you personally, and not healthy for your relationship. That's dependence (or codependence if it goes both ways), and that's not the same as simply missing someone when they're not around.

You can be 100% devoted to your partner and relationship but still be happy when the two of you are apart. A polyamorous relationship, or a person who has a whole other life completely separate from their partner, is not the only other option. You seem to be creating a false dichotomy here.

Pinning your happiness to the presence of another individual is not healthy. You cannot be with that person 100% of the time. And what if they die, or their feelings change and they don't want to be with you anymore? (Certainly either event would be devastating, but it should not destroy your only source of happiness.) How is it healthy for you to put all your emotional eggs in their basket? And even worse, how is it fair to the other person, to make that person an essential part of your constant happiness?