Couples are happy when they’re attracted to each other. Arguments turn bad is when the attraction is gone. Nobody wants to say “I’m not attracted to you anymore” so they fight dirty instead.
I think you're confusing necessary and sufficient conditions. The article isn't claiming that this argument style leads to happiness (ie, that it is sufficient), merely that other argument styles lead to unhappiness (ie, that it is necessary). But plenty of other things can go wrong along the way; just because you argue correctly doesn't mean you will have a happy relationship.
(Of course, whether or not it is actually necessary is open for debate.)
