The argument goes like this:
"I just don't think having more than one partner is fair to them. The love will never be equal, the relationships will never be equal."
I'll start by sparing you the Life's Not Fucking Fair, Grow The Fuck Up Speech*, and really cut to the quick on this argument. The person making this argument is starting from the false assumption that different relationships with different people are supposed to be the same. That the love you have for your mother is interchangable with the love you have for your father, both are parents, therefore it's only fair that the love be exactly the same.
Horseshit. Let's talk about something that really isn't fair (by which I mean just): expecting someone who's been seeing you for less than a year to prioritize you above (or even at the same level as) someone they've been seeing for 2 or 3 or 8 years. That's just not reasonable, regardless of whether it's just or fair or not. Not only is it unfair to expect to be equal to a new partner's other partners, it's not just or right or reasonable for a new partner to be made equal or the same as an established partner.
Oh, also: different people and different relationships are different. There's no comparing Ten to Jack! Pond to Eleven! Anyone to Nine! No comparisson because they are each individual persons with whom I have individual relationships, (and most of the poly folk I know run their shows this way), and when a person makes the mistake of comparing one relationship to another that's where drama starts.
Now, as a Timelord, with two hearts (you can count them), I love a little more, and more easily, than a lot of people I know. If I was to operate on this model where love between partners must always be equal I could never experience happiness in a relationship. I would not be able to count my friends because I wouldn't have any. The expectation that two different people could love or be loved in the same way or even the same amount is foolishness regardless of the context of the relationship. And if you do take into account the context of each relationship, that expectation becomes outright idiotic.
Of course, I've also said before that love is love is love, regardless of the context of the relationship. So, it doesn't really matter if you think it's fair or not.
*Guess what: life's not fucking fair. Grow the fuck up.