How does Felix connect to the thesis of The Odd Couple?

In The Odd Couple, Felix connects to the thesis of interpersonal relationships that is so dominant in the drama.
Felix is the countervailing force to Oscar.  Their relationship is predicated upon a balance.  Attributes of one offset the detriments of the other.  While Oscar spends money freely, Felix is financially controlling.  Oscar does not care about cleanliness, while Felix cares for little else.  Oscar cannot cook, yet Felix enjoys creating sumptuous meals in the kitchen.  The disorder of one matches the order of another.  While each is incapable of being effective on their own, when they are together, they make a whole.  In this way, Felix connects to the drama's thesis that relationships can be formed when people complement one another, compensating for the weaknesses of one with the strengths of another.
Another aspect of the interpersonal thesis that Simon illuminates is that excessive love of self can destroy relationships.  Oscar and Felix are single because their self-indulgence drove away their spouses.  Both were unable to overcome their own narcissism.  This prevented them from validating the other person.  Felix was overbearing to Frances, insistent that he could do things like cooking and cleaning better than she could.  Oscar drove Blanche away because his voice crowded out hers. Felix and Oscar demonstrate the dangers of being in a relationship without paying attention to the needs and wants of another person.  Through Felix and Oscar, Simon argues that no relationship can survive if reciprocity and mutual respect is lacking.  Interestingly enough, this becomes the reason why Felix and Oscar have to separate.  Neither one is capable of allowing the other's voice to flourish because they are so insistent on their own being dominant.  Simon's thesis is a warning to those in relationships who cannot see past their own needs.